1. Linear Algebra - Wikipedia, The Free Encyclopedia Linear algebra is a branch of mathematics concerned with the study of vectors, with families of vectors called vector spaces or linear spaces, http://en.wikipedia.org/wiki/Linear_algebra

Linear algebra From Wikipedia, the free encyclopedia Jump to: navigation search A line passing through the origin (blue, thick) in R is a linear subspace, a common object of study in linear algebra. Linear algebra is a branch of mathematics concerned with the study of vectors , with families of vectors called vector spaces or linear spaces , and with functions that input one vector and output another, according to certain rules. These functions are called linear maps (or linear transformations or linear operators) and are often represented by matrices . Linear algebra is central to modern mathematics and its applications. An elementary application of linear algebra is to the solution of a system of linear equations in several unknowns. More advanced applications are ubiquitous, in areas as diverse as abstract algebra and functional analysis . Linear algebra has a concrete representation in analytic geometry and is generalized in operator theory and in module theory . It has extensive applications in engineering physics natural sciences and the social sciences . Nonlinear mathematical models can often be approximated by linear ones.

2. Linear Algebra For Statistics Java Package Linear Algebra for Statistics Java Package. This package contains unofficial Java versions of many of the BLAS (Basic Linear Algebra Subroutines), and the LINPACK Cholesky http://www1.fpl.fs.fed.us/linear_algebra.html

FPL Statistics Group Linear Algebra for Statistics Java Package This package contains unofficial Java versions of many of the BLAS (Basic Linear Algebra Subroutines), and the LINPACK Cholesky decomposition (dpofa, dposl, and dpodi), QR decomposition (dqrdc and dqrsl), singular value decomposition (dsvdc), and LU decomposition (dgefa, dgesl, and dgedi) routines. The nonprofit Society for Industrial and Applied Mathematics (SIAM) sells copies of the LINPACK Users' Guide Other sources of Java linear algebra software: New as of 8/7/98: Numerical analysts at MathWorks and NIST have combined to produce a public domain Java linear algebra package called JAMA . (MathWorks maintains links to a variety of Java-based tools for science and engineering at http://www.mathtools.net/Java/index.html New as of 2/24/99: G.W. Stewart has produced a public domain Java linear algebra package called Jampack New as of 7/21/99: A US Government NIST (National Institute of Standards and Technology) site links to a wide variety of numerical Java resources. New as of 7/21/99: Links to proprietary Java linear algebra packages Warning!!! - Cholesky Decomposition - Warning!!!

3. Linear Algebra Linear algebra. Linear algebra is the branch of mathematics concerned with the study of vectorss, vector spaces (or linear spaces), linear transformations, and systems of http://www.fact-index.com/l/li/linear_algebra_1.html

Main Page See live article Alphabetical index Linear algebra Linear algebra is the branch of mathematics concerned with the study of vectorss , vector spaces (or linear spaces), linear transformations, and systems of linear equations . Vector spaces are a central theme in modern mathematics ; thus, linear algebra is widely used in both abstract algebra and functional analysis . Linear algebra also has a concrete representation in analytic geometry . It has extensive applications in the natural sciences and the social sciences See also Glossary of linear algebra Table of contents 1 History 2 Elementary Introduction 3 Some useful theorems 4 Generalisation and related topics ... 5 References History The history of modern linear algebra dates back to the years 1843 and 1844. In 1843, William Rowan Hamilton (from whom the term vector stems) discovered the quaternions . In 1844, Hermann Grassmann published his book Die lineare Ausdehnungslehre ... (for the complete title see References). to be continued k;k; Elementary Introduction Linear algebra had its beginnings in the study of vectors in Cartesian 2-space and 3-space. A vector, here, is a directed line segment, characterized by both length or magnitude and direction. Vectors can be used then to represent certain physical entities such as forces, and they can be added and multiplied with scalars, thus forming the first example of a real vector space.

4. Linear Algebra linear algebra program to perform computations with matrices, solution of linear systems, matrix operations, inverse, eigenvalues, eigenvectors, http://www.numericalmathematics.com/linear_algebra.htm

HOME Math Software Downloads Numerical Methods Register Your Software ... Credit Software Linear Algebra Functions Ordinary Differential Equations Systems of Nonlinear Equations ... Support Software Numerical Methods: Integration and Differentiation Solution of Equations Maxima and Minima Approximation of Functions ... Decimal Comma/Decimal Point Enter your search terms Submit search form Web www.numericalmathematics.com LINEAR ALGEBRA performs computations associated with real matrices, including solution of linear systems of equations (even least squares solution of over-determined or inconsistent systems and solution by LU factors), matrix operations (add, subtract, multiply), finding the determinant, trace, inverse, adjoint, QR and LU factors, eigenvalues and eigenvectors, establish the definiteness of a symmetric matrix, perform scalar multiplication, transposition, shift, create matrices of zeroes or ones, identity, symmetric or general matrices. Upon registering, you will receive by email a liberation key which will remove the registration reminder and the time limitation. You will be entitled to one year of free updates. Click here to download LINEAR ALGEBRA Requirements: Windows 98 or later AWARDS Click here to download LINEAR ALGEBRA Requirements: Windows 98 or later LINEAR ALGEBRA performs the following tasks: Add – Finds the sum of two matrices.

5. Linear Algebra - Wikimedia Labs, Collection Of Open-content Textbooks Linear algebra is a branch of mathematics concerned with the study of vectors, vector spaces, linear transformations, and systems of linear equations. http://en.labs.wikimedia.org/wiki/Linear_Algebra

Linear Algebra This page is brought to you by Wikimedia Laboratories Unchecked Jump to: navigation search This book requires Algebra as a prerequisite. This book is intended for readers at the Undergraduate level. Linear algebra is a branch of mathematics concerned with the study of vectors, vector spaces, linear transformations, and systems of linear equations. Vector spaces are very important in modern mathematics. Linear algebra is widely used in abstract algebra and functional analysis. It has extensive applications in natural and social sciences, for both linear systems and linear models of nonlinear systems. It is part of the study of Abstract algebra Contents Contents Determinants Vector Spaces Systems of Linear Equations ... edit Contents This book is part of a series on Algebra Algebra I (Simple) Algebra I Algebra Intermediate Algebra Linear Algebra Abstract Algebra Algebra 2 edit template TODO Complete table of contents edit Determinants Fields Systems of Linear Equations Matrices and Determinants Cofactors and Minors ... edit Vector Spaces Vector Spaces Linear Dependance Bases and dimensions Subspaces ... edit Systems of Linear Equations Row and column spaces Homogeneous Systems General Systems General Solutions ... edit Linear Transformations Linear transformations Matrices Invertible matrices The algebra of linear transformations ... edit Coordinate Transformations Basis Transformations Vector Transformations Linear Form Transformations Matrix Transformations ... edit Canonical Form Nilpotent Operators General Canonical Form Elementary Divisors Jordan Canonical Form ... edit Bilinear Form

6. Linear Algebra - Wikibooks, Collection Of Open-content Textbooks This book requires that you are familiar with Calculus. This subject is covered by the wikibook Calculus. http://en.wikibooks.org/wiki/Linear_Algebra

Linear Algebra From Wikibooks, the open-content textbooks collection Jump to: navigation search Linear Algebra An Introduction to Mathematical Discourse This book requires that you are familiar with Calculus. This subject is covered by the wikibook Calculus This book has a collection providing an on-demand PDF version as well as a printed book edit help A printable version of Linear Algebra is available in two parts. edit contains everything from the beginning of the book through Chapter III. edit contains everything from Chapter IV through the end of the book. The book was designed specifically for students who had not previously been exposed to mathematics as mathematicians view it. That is, as a subject whose goal is to rigorously prove theorems starting from clear consistent definitions. This book attempts to build students up from a background where mathematics is simply a tool that provides useful calculations to the point where the students have a grasp of the clear and precise nature of mathematics. A more detailed discussion of the prerequisites and goal of this book is given in the introduction. Table of Contents This book is part of a series on Algebra: Basic Algebra Algebra Intermediate Algebra Linear Algebra Abstract Algebra Intro to Rings and Algebras Cover Notation ... Introduction Linear Systems Solving Linear Systems Gauss' Method Describing the Solution Set General = Particular + Homogeneous ... Topic: Dimensional Analysis Maps Between Spaces Isomorphisms Definition and Examples Dimension Characterizes Isomorphism Homomorphisms ... Complex Representations Similarity

7. Linear Algebra - Uncyclopedia, The Content-free Encyclopedia Linear algebra, a branch of mathematics that describes spherical rooms (or vector room) of odd numbered dimensions (1,3,5, ,pi) described by curved vectors, subspheres http://uncyclopedia.wikia.com/wiki/Linear_Algebra

8. Linear Algebra Review Linear Algebra Review. Linear Algebra has become as basic and as applicable as calculus, and fortunately it is easier.Gilbert Strang. Most of digital signal processing can be http://www.ling.upenn.edu/courses/ling525/linear_algebra_review.html

Linear Algebra Review Linear Algebra has become as basic and as applicable as calculus, and fortunately it is easier. Gilbert Strang Most of digital signal processing can be seen as applied linear algebra. Therefore we begin with this brief review of linear algebra, and will return to the topic repeatedly. This introduction will also show you how to express each concept in Matlab. The Matlab examples will be in red fixed-width font. Note that the double "greater-than" is the Matlab prompt. Optional enrichment for those to whom a linear algebra review is old, boring stuff: The basic idea of abstract algebra, and of basing an algebra on directed magnitudes, seems to have been invented by Hermann Grassman , an interesting man who also worked on the tides, color vision, botany and Sanskrit, while teaching at a high school in Stettin (what it now Szczecin, Poland). He contributed his name to two laws (Grassmann's Laws of color vision and Grassmann's Law of aspiration dissimilation in Sanskrit and Greek), and wrote what is still the standard dictionary of Vedic Sanskrit. If the present review of standard linear algebra is old news to you, you can stimulate your imagination by learning about Grassmann/Clifford algebras and their applications in a set of lecture notes , in the amusingly-titled Imaginary Numbers are not Real and other works available on the web, including an application to

9. Kernel (matrix) - Wikipedia, The Free Encyclopedia In linear algebra, the kernel or null space (also nullspace) of a matrix A is the set of all vectors x for which Ax = 0. The kernel of a matrix with n columns is a linear subspace of n http://en.wikipedia.org/wiki/Kernel_(linear_algebra)

Kernel (matrix) From Wikipedia, the free encyclopedia   (Redirected from Kernel (linear algebra) Jump to: navigation search In linear algebra , the kernel or null space (also nullspace ) of a matrix A is the set of all vectors x for which Ax . The kernel of a matrix with n linear subspace of n -dimensional Euclidean space The dimension of the null space of A is called the nullity of A If viewed as a linear transformation , the null space of a matrix is precisely the kernel of the mapping (i.e. the set of vectors that map to zero). For this reason, the kernel of a linear transformation between abstract vector spaces is sometimes referred to as the null space of the transformation Contents Definition Example Subspace properties Basis ... edit Definition The kernel of an m n matrix A is the set where denotes the zero vector with m components. The matrix equation Ax is equivalent to a homogeneous system of linear equations From this viewpoint, the null space of A is the same as the solution set to the homogeneous system. edit Example Consider the matrix The null space of this matrix consists of all vectors ( x y z R for which This can be written as a homogeneous system of linear equations involving x y , and z This can be written in matrix form as: Using Gauss-Jordan reduction , this reduces to: Rewriting yields: Now we can write the null space (solution to Ax ) in terms of z (which is our free variable ), where z is

10. Linear Algebra 2008/9 Schools Wikipedia Selection. Related subjects Mathematics. Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear http://schools-wikipedia.org/wp/l/Linear_algebra.htm

Linear algebra 2008/9 Schools Wikipedia Selection . Related subjects: Mathematics Linear algebra is the branch of mathematics concerned with the study of vectors vector spaces (also called linear spaces linear maps (also called linear transformations ), and systems of linear equations . Vector spaces are a central theme in modern mathematics ; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry and it is generalized in operator theory. It has extensive applications in the natural sciences and the social sciences, since nonlinear models can often be approximated by linear ones. History William Rowan Hamilton introduced quaternions, which describe mechanics in three-dimensional space. In 1844, Hermann Grassmann published his book Die lineale Ausdehnungslehre (see References). Arthur Cayley introduced matrices , one of the most fundamental linear algebraic ideas, in 1857. Despite these early developments, linear algebra has been developed primarily in the twentieth century.

11. Linear Algebra - Simple English Wikipedia, The Free Encyclopedia Linear algebra describes ways to solve and manipulate (rearrange) systems of linear equations. For example consider the following equations These two equations form a system of linear http://simple.wikipedia.org/wiki/Linear_algebra

Linear algebra From Wikipedia, the free encyclopedia Jump to: navigation search Linear algebra describes ways to solve and manipulate (rearrange) systems of linear equations For example consider the following equations: These two equations form a system of linear equations. It is linear because none of the variables are raised to a power . The graph of a line ar equation is a straight line . The solution to this system is: since it makes all of the original equations valid, that is, the value on left side of the equals sign is exactly the same as the value on the right side for both equations. Linear algebra uses a system of notation for describing system behavior, called a matrix . For the previous example, the coefficients of the equations can be stored in a coefficient matrix. This short article about mathematics or a similar topic can be made longer. You can help Wikipedia by adding to it Retrieved from " http://simple.wikipedia.org/wiki/Linear_algebra Category Algebra Hidden category: Math stubs Personal tools New features Log in / create account Namespaces Page Talk Variants Views Read Change View history Actions Search Getting around Main Page Simple start Simple talk New changes ... Give to Wikipedia Print/export Make a book Download as PDF Page for printing Toolbox What links here Related changes Special pages Permanent link ... Cite this page In other languages Afrikaans Bosanski Català Česky ... Yorùbá This page was last changed on 28 September 2010, at 02:22.

12. Linear Algebra The dot product is an essential building block in linear algebra and for doing almost any type of transformation or rendering in computer graphics. http://www.cs.brown.edu/exploratories/freeSoftware/catalogs/linear_algebra.html

Exploratories Linear Algebra Navigation Home About Free Software Publications ... Help Catalogs Full Repository Repository Applets Repository Components Subject Catalogs Color Theory Viewing Techniques Signal Processing Texture Mapping ... Bezier Splines This applet introduces the user to the usage and mathematics of spline curves and includes a tutorial, exercises, and an interactive play space. Coordinate Transformations The Coordinate System Transformations applet teaches several concepts. The first is how a transformation applied to a coordinate system affects the axes of that coordinate system. Second, this applet shows how looking at only a very small portion of any curve produces a straight line (linear approximation) of that curve. Finally, this applet shows how a transformation of the coordinate system affects any objects within that coordinate system. Dot Product The Dot Product applet shows how the scalar dot product value of two vectors depends on both the vectors' lengths and the angle between them. It also demonstrates the dot product's property of rotational invariance. Editable equations are displayed, as are concept explanations and help text. The dot product is an essential building block in linear algebra and for doing almost any type of transformation or rendering in computer graphics. Normal Scaling 2D The 2D Surface Normals applet shows students how surface normals are affected by non-proportional (non-uniform) scaling. Without this knowledge, the shading of non-uniformly scaled objects is often calculated incorrectly.

13. LINEAR ALGEBRA WEBSITES Department of Mathematics, Massachusettes Institute of Technology This is a Linear Algebra course taught by Professor Gilbert Strang at MIT. http://www.math.ucdavis.edu/~daddel/linear_algebra_appl/OTHER_PAGES/other_pages.

LINEAR ALGEBRA WEBSITES Math Archives A great site for information and additional help. Help!!!!! Glossary Linear Algebra Glossary Vectors A great website to those having problems with vectors, dot product and scalar. Linear Algebra Tutorial Linear Algebra Visual Assistant, a site designed to help visualize linear Algebra. Help with Linear Algebra Intended to help students use the internet and programs such as Maple and Matlab for additional help. Dr. Mark Sapir's Linear Algebra Club Become part of this club. EkvSol v0.1 "Solve a system of linear equations, caculate the inverse matrix, calculate the determinat." Sample Exams and Notes Practice Exams Sample exams wirtten by Jeff O'connell Old Exams Here are some practice exams.. Department of Mathematics, Massachusettes Institute of Technology This is a Linear Algebra course taught by Professor Gilbert Strang at MIT. It includes study guides for finals and midterms ( useful for practice!!). Also matlab tutorial and matlab demos. Department of Mathematics, UC Berkeley Useful Notes and other links. Interesting Stuff Linear Algebra History How Linear algebra got started.

14. Linear Algebra File Format PDF/Adobe Acrobat http://www.comms.engg.susx.ac.uk/fft/math/Jim_Hefferon_-_Linear_Algebra.pdf

15. ELEMENTARY LINEAR ALGEBRA Feb 10, 2010 Elementary Linear Algebra by Keith Matthews. Lecture notes and solutions from 1991 in PDF or PostScript. http://www.numbertheory.org/book/

Elementary Linear Algebra (Lecture Notes by Keith Matthews CMAT : An exact arithmetic matrix calculator program Preface Title Page/Contents (pages 0, i-iv) pdf version of book Chapter 1: Linear Equations (pages 1-21) Chapter 2: Matrices (pages 23-54) Chapter 3: Subspaces (pages 55-69) Chapter 4: Determinants (pages 71-88) Chapter 5: Complex Numbers (pages 89-114) Chapter 6: Eigenvalues and Eigenvectors (pages 115-128) Chapter 7: Identifying Second Degree Equations (pages 129-148) Chapter 8: Three-dimensional Geometry (pages 149-187) Further Reading/Bibliography (pages 189,191-193) Index (pages 194-196) Corrections Solutions to Elementary Linear Algebra (Prepared by Keith Matthews, 1991) Title Page/Contents (pages 0/i) pdf version of the solutions (437K - best read with zoom in) Problems 1.6: Linear Equations (pages 1-11) Problems 2.4: Matrices (pages 12-17) Problems 2.7: Matrices (pages 18-31) Problems 3.6: Subspaces (pages 32-44) Problems 4.1: Determinants (pages 45-57) Problems 5.8: Complex Numbers (pages 58-68) Problems 6.3: Eigenvalues and Eigenvectors

16. Linear Algebra Textbook Home Page By Jim Hefferon. Free download in PDF and TeX source code. Covers the material of an undergraduate first linear algebra course. http://joshua.smcvt.edu/linearalgebra/

Linear Algebra by Jim Hefferon Mathematics Saint Michael's College Colchester, Vermont USA 05439 The text Linear Algebra is free for downloading, It covers the material of a first undergraduate Linear Algebra course. You can use it either as a main text, as a supplement to another text, or for independent study. What's Linear Algebra About? When I started teaching the subject I found three kinds of texts. There were applied mathematics books that avoid proofs and covered the linear algebra only as needed for their applications. There were advanced books that assumed students could understand their elegant proofs and also understand how to answer the homework questions having seen only one or two examples. And, there were books that spent a good part of the semester doing elementary things such as multiplying matrices and computing determinants, only to suddenly change level to working with definitions and proofs. Each of these three types was a problem in my classroom. The applications were interesting but I wanted to focus on the linear algebra. The advanced books were beautiful but my students were not ready for them. And, the level-switching books resulted in a great deal of grief. I took a level-switching book as an undergraduate, so I understood the struggle my students had with this. At the start of the semester they thought that these were like calculus books, where material labelled `proof' should be skipped in favor of the computational examples. Then, when the level switched, no amount of discussion on my part could convince students to switch with it, and the semester ended unhappily.

17. Elements Of Abstract And Linear Algebra By Edwin H. Connell An online textbook on abstract algebra with emphasis on linear algebra. http://www.math.miami.edu/~ec/book/

Elements of Abstract and Linear Algebra Edwin H. Connell This is a foundational textbook on abstract algebra with emphasis on linear algebra. You may download parts of the book or the entire textbook. It is provided free online in PDF DVI postscript , and gzipped postscript. Please read some words from the author first. Join the revolution in education! Write a supplement to this book and put it online. Participate in and contribute to a forum on abstract and linear algebra. Ask questions, give answers, and make comments in a worldwide classroom with the internet as blackboard. [March 20, 2004] The entire book Introduction Outline Chapter 1: Background and Fundamentals of Mathematics Chapter 2: Groups Chapter 3: Rings Chapter 4: Matrices and Matrix Rings Chapter 5: Linear Algebra Chapter 6: Appendix Index Please send comments to Edwin H. Connell Web page created by Dmitry Gokhman

18. Pauls Online Notes : Linear Algebra Here are my online notes for my Linear Algebra course that I teach here at Lamar University . Despite the fact that these are my “class notes”, http://tutorial.math.lamar.edu/Classes/LinAlg/LinAlg.aspx

MPBodyInit('LinAlg_files') Paul's Online Math Notes Online Notes / Linear Algebra You can navigate through this E-Book using the menu to the left. For E-Books that have a Chapter/Section organization each option in the menu to the left indicates a chapter and will open a menu showing the sections in that chapter. Alternatively, you can navigate to the next/previous section or chapter by clicking the links in the boxes at the very top and bottom of the material. Also, depending upon the E-Book, it will be possible to download the complete E-Book, the chapter containing the current section and/or the current section. You can do this be clicking on the E-Book Chapter , and/or the Section link provided below. For those pages with mathematics on them you can, in most cases, enlarge the mathematics portion by clicking on the equation. Click the enlarged version to hide it. E-Book Systems of Equations and Matrices Linear Algebra (Math 2318) Here are my online notes for my Linear Algebra course that I teach here at Lamar University .  Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Linear Algebra or needing a refresher.Â

19. Linear Algebra And Applications Textbook Textbook by Thomas Shores. GIFs of pages. http://www.math.unl.edu/~tshores1/linalgtext.html

Home Schedule Teaching Research ... Contact Me Linear Algebra and Applications Textbook Welcome again. In order to enable prospective users to preview my text easily and conveniently, in the past I have put a copy of it on the web for your perusal. In the last few years I've received many helpful comments and appreciative notes for having done so. I would like to thank those of you who sent me these notes and comments. You have helped me substantially improve the text. I am now under contract with Springer-Verlag and the book has been published in their Undergraduate Texts in Mathematics series in hardbound and, more recently, soft cover editions. Therefore, I have removed the on-line copy. I will leave the table of contents below for informational purposes, along with errata sheets for the each version of the textbook. A few comments: If you have any suggestions or comments, drop me a line. I appreciate any feedback. Resources A complete solutions manual to all exercises and problems in the text is available to instructors who have adopted the text. Instructors who would like a copy of this manual should contact Mark Spencer via email to Mark.Spencer@springer.com. For the benefit of instructors and students using my text, I'm moving a number of downloadable files on my website that pertain specifically to the text into their own directories. I also have complete solution keys to the exams and projects that are found in the directories below. I will email these to instructors who are using my text upon request. The text materials come in three flavors: pdf for perusal, lyx and tex for modification and use by instructors.

20. A First Course In Linear Algebra (A Free Textbook) A First Course in Linear Algebra Come for the price, stay for the quality http://linear.ups.edu/

A First Course in Linear Algebra Come for the price, stay for the quality nav_links('index'); A First Course in Linear Algebra is an introductory textbook designed for university sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Along the way, determinants and eigenvalues get fair time. PDF versions are available to download for printing or on-screen viewing, two online versions are available, and physical copies may be purchased from the print-on-demand service at Lulu.com It seems therefore desirable to give permanent form to the lessons of experience so that others can benefit by them and be encouraged to undertake similar work. H.M. Cundy and A.P. Rollet, Mathematical Models, 1952 This textbook has more freedom than most (but see some exceptions GNU Free Documentation License (GFDL). It is this combination that allows

Page 1     1-20 of 129    1  | 2  | 3  | 4  | 5  | 6  | 7  | Next 20