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	Matrix Math
		Because of the above (matrix 1 width = matrix 2 height) transformation matrices are therefore square, - 3x3 or 4x4 are commonly used for 3D transformations.
		The inverse of a matrix is a matrix of the same size, which undoes any transformation performed by the original matrix.
		You calculate the determinant of the submatrix, divide that by the determinant of the matrix (not the submatrix), and multiply by
	easyweb.easynet.co.uk /~mrmeanie/matrix/matrices.htm (0 words)

	PlanetMath: matrix inverse
		Some caveats: computing the matrix inverse for ill-conditioned matrices is error-prone; special care must be taken and there are sometimes special algorithms to calculate the inverse of certain classes of matrices (for example, Hilbert matrices).
		The need to find the matrix inverse depends on the situation- whether done by hand or by computer, and whether the matrix is simply a part of some equation or expression or not.
		However, the matrix inverse may exist in the case of the elements being members of a commutative ring, provided that the determinant of the matrix is a unit in the ring.
	planetmath.org /encyclopedia/MatrixInverse.html (464 words)

	Matrix Maths (Site not responding. Last check: )
		The restriction for this is that the rows in the first matrix must be the same length as the columns in the second column.
		Scaling a matrix is simply a matter of multiply each element of the matrix by the same scaling value, this results in a matrix of exactly the dimensions as the original.
		Due to the need for combining matricies transformations so only one matrix need to executed to perform many transformations, the other operations such as scaling which could be done using 3x3 matricies must be converted to 4x4 matricies.
	www.kraftwrk.com /resources/matrixmath/tut_main.htm (1044 words)

	Matrix Transformation (Site not responding. Last check: )
		Math Prerequisites Sadly, matrix math is something that is all but ignored in most high school curricula in the United States.
		Matrix Multiplication There are two matrix operations which we will use in our matrix transformations, multiplying (concatenating) two matrices, and transforming a vector by a matrix.
		Matrix multiplication is the operation by which one matrix is transformed by another.
	www.whisqu.se /per/docs/math22.htm (4220 words)

	Matrix Multiplication: How to Multiply Two Matrices Together
		Matrix C and D below cannot be multiplied together because the number of columns in C does not equal the number of rows in D. In this case, the multiplication of these two matrices is not defined.
		Since the number of columns in Matrix A does not equal the number of rows in Matrix B. The multiplication of A and B is undefined.
		The product matrix's dimensions are 2 • 3 since there are two rows in the first matrix (Matrix A) and three columns in the second matrix (matrix B).
	www.mathwarehouse.com /algebra/matrix/multiply-matrix.php (429 words)

	Matrix math (Site not responding. Last check: )
		A square matrix is a matrix that has the same number of rows and columns.
		The matrix in the first example above is not a square matrix; the matrices in the second equation are square.
		Matrix multiplication is not as simple and intuitive as matrix addition.
	library.thinkquest.org /16500/FiniteMath/matrix1.html (420 words)

	Fusion Industries :: Crash Course in Linear Algebra ::
		We refer to each element by calling it Mij, where M is the matrix, i is the row number and j is the column number.
		For a given row in the first matrix A and a given column in the second matrix B, multiply each component in A with B and add the results.
		The inverse of a matrix is noted as A^-1.
	www.fusionindustries.com /default.asp?page=matrixmath (1165 words)

	Matrix (math) - Uncyclopedia, the content-free encyclopedia
		A matrix is a long list of numbers that can be used to describe at least a zillion different things.
		A matrix of order n (where n is a number 1,2,pi,4,5,...) an be added with another matrix of order m (where m is another number, possibly the same as n, or larger, or smaller, and I'm not talking about the font size).
		The practical applications of this type of math is left to the reader to evaluate as an exercise.
	uncyclopedia.org /wiki/Matrix_(math) (462 words)

	Math::MatrixBool - Matrix of Booleans
		Computing the closure of this matrix means to find out if there is a path from any vortice of the graph to any other (a path consisting of one or more edges).
		I.e., the number of columns of matrix #1 is the same as the number of rows of matrix #2, and the number of rows and columns of the resulting matrix #3 is determined by the number of rows of matrix #1 and the number of columns of matrix #2, respectively.
		This way you can also perform the multiplication of a matrix with a vector, since a vector is just a degenerated matrix with several rows but only one column, or just one row and several columns.
	www.aist-nara.ac.jp /~masa-n/misc/cmc/perltk/quick/html/site/lib/Math/MatrixBool.html (2269 words)

	Math 120 Row Reduction
		Enter the dimensions of the matrix at the top if the dimensions are incorrect.
		Since you are working with matrix A, that is the matrix you will select.
		Matrix A is already selected as the default.
	lilt.ilstu.edu /cheri/math120/Math120RowReduction.htm (268 words)

	3D:Matrix Math - GPWiki
		We arrive at a matrix that does a translation of (4 4 4), which is exactly what you'd expect the result of combining two (2 2 2) translations to be.
		When this matrix is the identity matrix, points are not transformed and the world is oriented in some default position (for OpenGL this means the camera is at (0 0 0) looking down the Z-axis.
		Note that this will clobber the matrix and when you draw another object you'll want to undo the transformations that were specific to the previous object, but not those that position the camera.
	gpwiki.org /index.php/3D:Matrix_Math (1048 words)

	Matrix Reference Manual
		Thus [1 2 3; 4 5 6] is a matrix with 2 rows and 3 columns.
		ADJ(A) is the adjoint of the square matrix A.
		DIAG(a) is the diagonal matrix whose diagonal elements are the elements of a.
	www.ee.ic.ac.uk /hp/staff/dmb/matrix/intro.html (1367 words)

	GameDev.net - Matrix Math
		Matrix math is commonly used in 3D engines, unfortunately, I haven't found any tutorials on matrix math itself.
		In 3D math, we typically use a 4x4 matrix, which is analogous to a 4x4 array.
		If you want to perform all the operations in the final matrix to a 3D point, all you must do is multiply the matrix and the point.
	www.gamedev.net /reference/articles/article877.asp (0 words)

	Math::MatrixReal - Matrix of Reals
		One formula for the inverse of a matrix is the cofactor matrix transposed divided by the original determinant of the matrix.
		An orthogonal matrix is has the property that the transpose equals the inverse of the matrix.
		However, as soon as you are applying any method that alters the contents of the matrix, its ``magical'' properties are stripped off, and the matrix immediately reverts to an ``ordinary'' matrix (with the values it just happens to contain at that moment, be they meaningful as an ordinary matrix or not!).
	www.leto.net /code/Math-MatrixReal/man.html (7699 words)

	Ed Pegg's Math Games - Matrix Revolutions
		A matrix, very simply, is a rectangular array of numbers.
		The matrix B is a rotation matrix, which rotates the given point p in an arc centered on the origin, {0,0}.
		In the third image, a translation matrix was added at each step, which resulted in a more elliptical spiral.
	www.maa.org /editorial/mathgames/mathgames_11_10_03.html (966 words)

	Using MATRIX on the TI-83
		The matrix menu is quite extensive and an exhaustive study here is beyond the scope of this tutorial.
		The example below will take you through the basic steps of entering a matrix and using it to solve a system of equations, which is one of the main applications of matrices that you will use in an algebra course.
		To use a matrix to solve a system of equations, you put the matrix in reduced row echelon form.
	www.prenhall.com /divisions/esm/app/graphing/ti83/Home_Screen/Menu_Keys/Matrix/matrix.html (240 words)

	The Math Forum - Math Library - Matrices (Site not responding. Last check: )
		A computer-based course about calculus, differential equations, and matrix theory, which the instructor can use as soon as the computers are unloaded at the classroom door.
		A matrix calculator program, written in C. Calculations can be performed on matrices with rational, complex rational coefficients using exact arithmetic routines, as well as on matrices with elements mod p.
		A free matrix algebra book in PDF format for freshman engineering and science students who do not take a formal course in numerical methods or take matrix algebra as a part of another course such as Numerical Methods or Differential Equations.
	mathforum.org /library/topics/matrices (2160 words)

	Dr. Dobb's \| Math.h++ Library \| April 15, 2003
		For example, given a matrix A, the following code produces a matrix in which each element in B is the absolute value of the corresponding element in A.
		To form matrix picks, you specify a set of rows (a vector of integers) and a set of columns (another vector of integers).
		For example, the only difference between a float matrix class and a double matrix class is probably that each occurrence of the key word float is replaced by the key word double.
	www.ddj.com /184402240?pgno=1 (2473 words)

	An introduction to MATRICES
		A diagonal matrix is a square matrix with all de non-diagonal elements 0.
		[7 0 0] [0 5 0] [0 0 6] The matrix is denoted by diag(7, 5, 6)
		An identity matrix I is a diagonal matrix with all diagonal element = 1.
	www.ping.be /~ping1339/matr.htm (921 words)

	Math Forum Discussions (Site not responding. Last check: )
		Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
		Math Forum » Discussions » sci.math.* » sci.math
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /kb/thread.jspa?threadID=107234&messageID=552066 (127 words)

	Tech Matrix - The gateway site to the NCTI Reading and CITED Math Matrices
		Disclaimer: The Tech Matrix contains information from other public and private organizations that may be useful to the reader; these materials are merely examples of resources that may be available.
		To search a matrix database of products and evidence, select one of the six purposes of technology that support math or reading for students with special needs.
		These matrices are intended to serve as resources that match technology tools with supporting literature on promising practices for the instruction of K-8 mathematics and reading for students with disabilities.
	www.techmatrix.org (210 words)

	Maths - Matrix algebra and 3D transformation - Martin Baker
		A matrix is a rectangular array of elements which are operated on as a single object.
		With matrix multiplication each element is the dot product of a row from one matrix and the column from the other matrix (see matrix arithmetic) Perhaps it would work if the second matrix to be multiplied were transposed first?
		A matrix is a way to transform one vector into another vector (and a whole set of vectors into another set of vectors).
	www.euclideanspace.com /maths/algebra/matrix/index.htm (718 words)

	Matrix Math Libraries (Site not responding. Last check: )
		Matrix Math Library Readme These C Routines implement 2D matrix math for geometric transformations.
		The matrix math library uses both low level routines and globals and high level routines that set and access the globals.
		The matrix math uses a vector graphics library which I lifted with minor modifications from the Graphics Gems 1 & 2 code.
	collaboratory.nunet.net /phertz/code/matxmath.html (349 words)

	Matrix Transformations - 3DSoftware.com
		Matrix algebra is a part of linear algebra that is used extensively in computer graphics programming.
		When specifying the order of a matrix, the first number is the number of rows in the matrix, and the second number is the number or columns.
		Each row in a matrix can be thought of as a row vector, and each column can be thought of as a column vector.
	www.3dsoftware.com /Math/MatrixTransformations (1031 words)

	HelpSpy: Math::Matrix CPAN (Perl) Module Help
		This is the matrix where colums and rows of the argument matrix are swaped.
		Multiplies two matrices where the length of the rows in the first matrix is the same as the length of the columns in the second matrix.
		Multiplies a matrix and a scalar resulting in a matrix of the same dimensions with each element scaled with the scalar.
	helpspy.com /c.m/programming/lang/perl/cpan/c06/Math/Matrix (309 words)

	Matrix Basics - Math and Statistics Library for C# and VB.NET: BLAS, LAPACK, more
		A symmetric matrix is equal to its transpose.
		A method call on a matrix has no effect on whether the instance is a stand-alone or a derived matrix.
		In all cases, the components of the new matrix are guaranteed to be stored in a contiguous block of memory.
	www.extremeoptimization.com /mathematics/usersguide/matrices/matrixBasics.aspx (1099 words)

	Matrix Math (Site not responding. Last check: )
		> >Generally the inverse is found by writing the identity matrix beside the >matrix you want to find the inverse of, and then attempting to transform the >matrix into the identity matrix, while performing the same operations on the >identity matrix.
		When you are done, the original matrix >should be the identity matrix, and the original identity matrix will be the >inverse.
		A triangular matrix is either upper or >lower triangular.
	www.newton.dep.anl.gov /askasci/math99/math99083.htm (545 words)

	Dr. Matrix at the Scientium: Mathematics Links (Site not responding. Last check: )
		Cornell Theory Center Math and Science Gateway - The Cornell Theory Center Math and Science Gateway is a service of the Cornell Theory Center which is committed to providing a wide range of educational services to the national community.
		E-GEMS : Electronic Games for Education in Math and Science - The E-GEMS project is a collaborative effort by scientists, educators, and professional video game and educational software developers who have come together to do research on and develop teaching materials that integrate video games and computer-based explorations with existing classroom practices.
		The aim of this research is to increase the proportion of children in Grades 4-8 who enjoy learning, mastering, and using underlying concepts of math and science.
	www.scientium.com /drmatrix/sciences/math.htm (1411 words)

	matrix - Definitions from Dictionary.com
		matrice, from L. matrix (gen. matricis) "pregnant animal," in L.L. "womb," also "source, origin," from mater (gen. matris) "mother." Sense of "place or medium where something is developed" is first recorded 1555; sense of "embedding or enclosing mass" first recorded 1641.
		Bone cells are embedded in a matrix of collagen fibers and mineral salts.
		The name of the rather good 1999 cypherpunk movie "The Matrix" played on this sense, which however had been established for years before.
	dictionary.reference.com /browse/matrix (1422 words)

	Matrix and Quaternion FAQ (Site not responding. Last check: )
		A matrix with M rows and N columns is defined as a MxN matrix.
		The inverse of an identity matrix is the identity matrix.
		In this case, the value of each matrix element is defined by: -1 1 i+j M = ----- * det submat M * -1 j,i det M i,j Q22.
	www.flipcode.com /documents/matrfaq.html (7478 words)

	Matrix and Linear Algebra
		All matrix elements are set to zero except those of the diagonal which are filled sequentially from elements of waveA.
		If matrixA is not a square matrix, the sum is over the elements for which the row and column indices are the same.
		Returns a tri-diagonal matrix where w1 is the upper diagonal, w2 the main diagonal and w3 the lower diagonal.
	www.wavemetrics.com /products/igorpro/datamanipulation/matrixmath.htm (1739 words)

	Programming 2D Computer Graphics > Using Matrix Math in Transformations (Site not responding. Last check: )
		A matrix can be multiplied by any other matrix as long as the first matrix has the same number of columns as the second matrix has rows.
		So a 1x3 matrix can be multiplied by a 3x3 matrix, which is fortunate because that's exactly what you need to do to multiply a matrix times a vector in 2D graphics programs.
		An identity matrix is often used in graphics programming to initialize the main matrix that'll be used to compose transformations.
	www.informit.com /articles/article.asp?p=98117&seqNum=4 (2275 words)

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