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1. Matrix (mathematics) - Wikipedia, The Free Encyclopedia
matrices are a key tool in linear algebra. One use of matrices is to represent linear transformations, which are higherdimensional analogs of linear
http://en.wikipedia.org/wiki/Matrix_(mathematics)
##### Matrix (mathematics)
From Wikipedia, the free encyclopedia Jump to: navigation search Specific entries of a matrix are often referenced by using pairs of subscripts. In mathematics , a matrix (plural matrices , or less commonly matrixes ) is a rectangular array of numbers , such as An item in a matrix is called an entry or an element. The example has entries 1, 9, 13, 20, 55, and 4. Entries are often denoted by a variable with two subscripts , as shown on the right. Matrices of the same size can be added and subtracted entrywise and matrices of compatible sizes can be multiplied . These operations have many of the properties of ordinary arithmetic, except that matrix multiplication is not commutative , that is, AB and BA are not equal in general. Matrices consisting of only one column or row define the components of vectors , while higher-dimensional (e.g., three-dimensional) arrays of numbers define the components of a generalization of a vector called a tensor . Matrices with entries in other fields or rings are also studied. Matrices are a key tool in linear algebra . One use of matrices is to represent linear transformations , which are higher-dimensional analogs of linear functions of the form f x cx where c is a constant; matrix multiplication corresponds to

2. Algebra II: Matrices - Math For Morons Like Us
On this page we hope to clear up problems that you might have with matrices. matrices are good things to have under control and know how to deal with,
http://library.thinkquest.org/20991/alg2/matrices.html
 Systems of Eq. Polynomials Frac. Express. Complex Numbers ... Trig. Identities On this page we hope to clear up problems that you might have with matrices. Matrices are good things to have under control and know how to deal with, because you will use them extensively in pre-calculus to solve systems of equations that have variables up the wazoo! (Like one we remember with seven equations in seven variables.) Addition and subtraction Multiplication Quiz on Matrices To add matrices, we add the corresponding members. The matrices have to have the same dimensions. Example: Solution: Add the corresponding members. Subtraction of matrices is done in the same manner as addition. Always be aware of the negative signs and remember that a double negative is a positive! Back to Top You can multiply a matrix by another matrix or by a number. When you multiply a matrix by a number, multiply each member of the matrix by the number. To multiply a matrix by a matrix, the first matrix has to have the same number of columns as the rows in the second matrix. Examples: Solution: Multiply each member of the matrix by 2. Problem: Multiply the matrices shown below.

3. S.O.S. Math - Matrix Algebra
Introduction to Determinants Determinants of matrices of Higher Order Determinant and Inverse of matrices Application of Determinant to Systems
http://www.sosmath.com/matrix/matrix.html
 S.O.S. Homepage Algebra Trigonometry Calculus ... CyberBoard Search our site! S.O.S. Math on CD Sale! Only \$19.95. Works for PCs, Macs and Linux. Tell a Friend about S.O.S. Books We Like Math Sites on the WWW S.O.S. Math Awards ... Matrix Exponential Applications: Systems of Linear Equations Determinants Eigenvalues and Eigenvectors APPENDIX Contact us Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA users online during the last hour

4. 4. Multiplication Of Matrices
Sep 18, 2010 This section shows you how to multiply matrices of different dimensions. Includes a Flash interactive.
http://www.intmath.com/Matrices-determinants/4_Multiplying-matrices.php
This is interactive mathematics
where you learn math by playing with it!
##### Chapter Contents
Get the Daily Math Tweet!
##### Recommendation
Easy to understand algebra lessons on DVD. Try before you commit. More info:
MathTutorDVD.com
##### Where did matrices and determinants come from?
M Many of our mathematical discoveries are named after European mathematicians, even though they originated in China, India or the Middle East. Gaussian Elimination is one example....
##### Algebrator review
Algebrator is an interesting product - but I'm not sure that I can recommend it....
##### The Twelve Days of Christmas - How Many Presents?
What is the math behind the "12 Days of Christmas" song?...
##### Summation notation
Yousuf has trouble understanding a question involving summation notation. After some effort, he gets there!...

 5. Lessons On Matrices (with Worked Solutions & Videos) matrices (singular matrix, plural matrices) have many uses in real life. One application would be to use matrices to represent a large amount of data in ahttp://www.onlinemathlearning.com/matrices-lessons.html

6. Matrix -- From Wolfram MathWorld
Oct 11, 2010 In this work, matrices are represented using square brackets as delimiters, Two matrices may be added (matrix addition) or multiplied
http://mathworld.wolfram.com/Matrix.html
 Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Interactive Demonstrations Matrix A matrix is a concise and useful way of uniquely representing and working with linear transformations . In particular, every linear transformation can be represented by a matrix, and every matrix corresponds to a unique linear transformation . The matrix, and its close relative the determinant , are extremely important concepts in linear algebra , and were first formulated by Sylvester (1851) and Cayley. In his 1851 paper, Sylvester wrote, "For this purpose we must commence, not with a square, but with an oblong arrangement of terms consisting, suppose, of lines and columns. This will not in itself represent a determinant , but is, as it were, a Matrix out of which we may form various systems of determinants by fixing upon a number , and selecting at will lines and columns, the squares corresponding of th order." Because Sylvester was interested in the determinant formed from the rectangular array of number and not the array itself (Kline 1990, p. 804), Sylvester used the term "matrix" in its conventional usage to mean "the place from which something else originates" (Katz 1993). Sylvester (1851) subsequently used the term matrix informally, stating "Form the rectangular matrix consisting of rows and columns.... Then all the

7. Introduction To Matrices / Matrix Size
Defines matrices and basic matrix terms, illustrating these terms with worked solutions to typical homework exercises.
http://www.purplemath.com/modules/matrices.htm
 The Purplemath Forums Helping students gain understanding and self-confidence in algebra powered by FreeFind Return to the Lessons Index Do the Lessons in Order Get "Purplemath on CD" for offline use ... Print-friendly page Introduction to Matrices / Matrix Size (page 1 of 3) Matrix equality Augmented matrices Matrices are incredibly useful things that crop up in many different applied areas. For now, you'll probably only do some elementary manipulations with matrices, and then you'll move on to the next topic. But you should not be surprised to encounter matrices again in, say, physics or engineering. (The plural "matrices" is pronounced as "MAY-truh-seez".) Matrices were initially based on systems of linear equations Given the following system of equations, write the associated augmented matrix. x y z x y z x y z Write down the coefficients and the answer values, including all "minus" signs. If there is "no" coefficient, then the coefficient is " ".

 8. Matrices File Format PDF/Adobe Acrobat Quick Viewhttp://www.mathworks.com/moler/exm/chapters/matrices.pdf

9. Matlab
Matlab Matlab is a tool for doing numerical computations with matrices and vectors. It can also display information graphically. The best way to learn what
http://www.math.utah.edu/lab/ms/matlab/matlab.html
##### Matlab
Matlab is a tool for doing numerical computations with matrices and vectors. It can also display information graphically. The best way to learn what Matlab can do is to work through some examples at the computer . After reading the " getting started " section, you can use the tutorial below for this.
• Getting started Tutorial
##### Getting started
Here is a sample session with Matlab. Text in bold is what you type, ordinary text is what the computer "types." You should read this example, then imitate it at the computer. matlab a = [ 1 2; 2 1 ] a*a quit 16 flops. % In this example you started Matlab by (you guessed it) typing matlab . Then you defined matrix a and computed its square ("a times a"). Finally (having done enough work for one day) you quit Matlab. The tutorial below gives more examples of how to use Matlab. For best results, work them out using a computer: learn by doing!

 10. Matrices - Definition Of Matrices By The Free Online Dictionary, Thesaurus And E ma tri ces (m trs z, m t r-) n. A plural of matrix. matrices ˈmeɪtrɪˌsiːz ˈm - n (Life Sciences Allied Applications / Anatomy) (Life Sciences Allied Applications / Biologyhttp://www.thefreedictionary.com/matrices

11. Matrices.net
Welcome to www.matrices.net! My name is Sara Howard, I'm also known as matrices. This site is divided into four sections About Me
http://matrices.net/
 Welcome to www.matrices.net ! My name is Sara Howard, I'm also known as Matrices. This site is divided into four sections: "About Me" which is a short autobiography. "Art" which is a showcase of what I consider my artwork (including drawings and crafts). "Costuming" which is a resource on how I built my own costumes, with tutorials on you how you can do it, too! And "Other Stuff" which includes links, my journal, and anything else. Thank you for visiting, I hope you enjoy your stay. Go ahead and explore the site and have fun! people have visited this site since July 21st 2001. Important message I had an excellent time at Rainfurrest 2010, as promised I am providing the handouts I produced for my Rainfurrest panels, right here as a part of my website! Please enjoy these newest articles: Video section updated with video from one of my panels I hosted with one of my friends at Rainfurrest!

12. Mathematical Structure -- Matrices
You should use one of the computer algebra systems below with this module. Click on the appropriate icon for your preferred CAS and then arrange your screen so that you can
http://www.math.montana.edu/frankw/ccp/multiworld/building/matrix/refer.htm
##### Mathematical Structure Matrices
Prerequisites: You should use one of the computer algebra systems below with this module. Click on the appropriate icon for your preferred CAS and then arrange your screen so that you can easily move back-and-forth between this window and your CAS window. Click on the appropriate help button for help. An (n by k)-matrix is an array or table of numbers with n rows and k columns for example, the matrices below each have two rows and three columns. Notice that we usually use capital letters to denote entire matrices and the corresponding small letter with two subscripts to denote the entries in a matrix. The first subscript denotes the row and the second subscript denotes the column. For example, the entry in the second row and third column of the matrix M above is m The set of (n by k) - matrices is a vector space with vector addition and scalar multiplication defined by The zero vector in this vector space is the (n by k)-matrix with all zero entries. Do each of the following calculations "by hand" and then check your answer in your CAS window.

13. Matrices In Matlab
A basic introduction to defining and manipulating matrices is given here. It is assumed that you know the basics on how to define and manipulate vectors
http://www.cyclismo.org/tutorial/matlab/matrix.html
##### Cyclismo.org
More Tutorials:
Front Page

vectors

matrices

vector operations
...
data files
##### Introduction to Matrices in Matlab
A basic introduction to defining and manipulating matrices is given here. It is assumed that you know the basics on how to define and manipulate vectors using matlab.
• Defining Matrices Matrix Functions Matrix Operations
• ##### Defining Matrices
Defining a matrix is similar to defining a vector . To define a matrix, you can treat it like a column of row vectors (note that the spaces are required!): You can also treat it like a row of column vectors: (Again, it is important to include the spaces.) If you have been putting in variables through this and the tutorial on vectors , then you probably have a lot of variables defined. If you lose track of what variables you have defined, the whos command will let you know all of the variables you have in your work space. We assume that you are doing this tutorial after completing the previous tutorial. The vector v was defined in the previous tutorial. As mentioned before, the notation used by Matlab is the standard linear algebra notation you should have seen before. Matrix-vector multiplication can be easily done. You have to be careful, though, your matrices and vectors have to have the right size!

A library of Hadamard matrices maintained by N. J. A. Sloane.
##### N. J. A. Sloane
Keywords : Hadamard matrices, Kimura matrices Paley matrices, Plackett-Burman designs, Sylvester matrices, Turyn construction, Williamson construction
• Contains all Hadamard matrices of orders n up through 28, and at least one of every order n up through 256. This library is maintained by N. J. A. Sloane njas@research.att.com Notation:
• had.n.name indicates a Hadamard matrix of order n and type "name". The matrices are usually given as n rows each containing n +'s and -'s (with no spaces). In many cases there are further rows giving the name of the matrix and the order of its automorphism group.
What the suffixes mean:
• od = orthogonal design construction method pal = first Paley type pal2 = second Paley type syl = Sylvester type tur = Turyn type tx = tensor product of type x with ++/+- or (rarely) with a Hadamard matrix of order 4 will = Williamson type
References:
• Seberry, J. and Yamada, M., Hadamard matrices, sequences, and block designs , pp. 431-560 of Dinitz, J. H. and Stinson, D. R., editors (1992), Contemporary Design Theory: A Collection of Essays, Wiley, New York. Chapter 7 of Orthogonal Arrays by Hedayat, Sloane and Stufken.

 15. SparkNotes: Matrices From a general summary to chapter summaries to explanations of famous quotes, the SparkNotes matrices Study Guide has everything you need to ace quizzes, tests, and essays.http://www.sparknotes.com/math/algebra2/matrices/

16. An Introduction To MATRICES
Definitions Matrix. A matrix is an ordered set of numbers listed rectangular form. Example. Let A denote the matrix 2 5 7 8 5 6 8 9 3 9 0 1
http://www.ping.be/~ping1339/matr.htm
##### An introduction to MATRICES
• Definitions
##### Matrix
A matrix is an ordered set of numbers listed rectangular form. Example. Let A denote the matrix This matrix A has three rows and four columns. We say it is a 3 x 4 matrix. We denote the element on the second row and fourth column with a
##### Square matrix
If a matrix A has n rows and n columns then we say it's a square matrix. In a square matrix the elements a i,i , with i = 1,2,3,... , are called diagonal elements.
Remark. There is no difference between a 1 x 1 matrix and an ordenary number.
##### Diagonal matrix
A diagonal matrix is a square matrix with all de non-diagonal elements 0.
The diagonal matrix is completely denoted by the diagonal elements.
Example. [7 0] [0 5 0] [0 6] The matrix is denoted by diag(7 , 5 , 6)
##### Row matrix
A matrix with one row is called a row matrix
##### Column matrix
A matrix with one column is called a column matrix
##### Matrices of the same kind
Matrix A and B are of the same kind if and only if
A has as many rows as B and A has as many columns as B
##### The tranpose of a matrix
The n x m matrix A' is the transpose of the m x n matrix A if and only if
The ith row of A = the ith column of A' for (i = 1,2,3,..n)

17. Emma's Final Year Project
DEFINITION Two matrices A and B can be added or subtracted if and only if their dimensions are the same (i.e. both matrices have the same number of rows
http://www.maths.surrey.ac.uk/explore/emmaspages/option1.html
##### Introduction and Examples
DEFINITION: A matrix is defined as an ordered rectangular array of numbers. They can be used to represent systems of linear equations, as will be explained below. Here are a couple of examples of different types of matrices: Symmetric Diagonal Upper Triangular Lower Triangular Zero Identity ... or in a more compact form: Top
DEFINITION: Two matrices A and B can be added or subtracted if and only if their dimensions are the same (i.e. both matrices have the same number of rows and columns. Take:
If A and B above are matrices of the same type then the sum is found by adding the corresponding elements a ij b ij Here is an example of adding A and B together.
##### Subtraction
If A and B are matrices of the same type then the subtraction is found by subtracting the corresponding elements a ij b ij Here is an example of subtracting matrices. Now, try adding and subtracting your own matrices.

18. Matrix (mathematics)
Matrix (mathematics) In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, of elements of a fixed ring.
http://www.fact-index.com/m/ma/matrix__mathematics_.html
Main Page See live article Alphabetical index
##### Matrix (mathematics)
In mathematics , a matrix (plural matrices ) is a rectangular table of numbers or, more generally, of elements of a fixed ring . In this article, if unspecified, the entries of a matrix are always real or complex numbers. Matrices are useful to record data that depends on two categories, and to keep track of the coefficients of systems of linear equations and linear transformations. For the development and applications of matrices, see matrix theory The term is also used in other areas, see matrix Table of contents 1 History
2 Definitions and Notations

2..1 Matrices with entries in arbitrary rings

2..2 Partitioning Matrices
...
7 Glossary and related topics
##### History
See Matrix theory
##### Definitions and Notations
The horizontal lines in a matrix are called rows and the vertical lines are called columns . A matrix with m rows and n columns is called an m -by- n matrix (or m n matrix) and m and n are called its dimensions . For example the matrix below is a 4-by-3 matrix: The entry of a matrix A that lies in the i th row and the j -th column is called the i,j

19. Homogeneous Transformation Matrices
Explicit n-dimensional homogeneous matrices for projection, dilation, reflection, shear, strain, rotation and other familiar transformations.
http://www.silcom.com/~barnowl/HTransf.htm
 HOMOGENEOUS TRANSFORMATION MATRICES Daniel W. VanArsdale NOTE: I am seeking a permanent institutional host for this web page, and the related Homogeneous Coordinates: Methods. This site, "Homogeneous Transformation Matrices" has received over 110,000 hits since the year 2000. It is linked to by many sources. Contact Author: Daniel VanArsdale Vector (nonhomogeneous) methods are still being recommended to effect rotations and other linear transformations. Homogeneous matrices have the following advantages: simple explicit expressions exist for many familiar transformations including rotation these expressions are n-dimensional there is no need for auxiliary transformations, as in vector methods for rotation more general transformations can be represented (e.g. projections, translations) directions (ideal points) can be used as parameters of the transformation, or as inputs if nonsingular matrix T transforms point P by PT, then hyperplane h is transformed by T h the columns of T (as hyperplanes) generate the null space of T by intersections many homogeneous transformation matrices display the duality between invariant axes and centers.

20. Matrix - Wikipedia, The Free Encyclopedia
Pauli matrices, a set of matrices in physics named for Wolfgang Pauli; Technology. Multistate AntiTerrorism Information Exchange (MATRIX), a database of US Citizens
http://en.wikipedia.org/wiki/Matrices