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Topic: Matrix addition

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	Matrix (mathematics) - Wikipedia, the free encyclopedia
		The entry of a matrix A that lies in the i -th row and the j-th column is called the i,j entry or (i,j)-th entry of A.
		The rank of a matrix A is the dimension of the image of the linear map represented by A; this is the same as the dimension of the space generated by the rows of A, and also the same as the dimension of the space generated by the columns of A.
		The trace of a square matrix is the sum of its diagonal entries, which equals the sum of its n eigenvalues.
	en.wikipedia.org /wiki/Matrix_(mathematics) (1577 words)

	Matrix addition - Wikipedia, the free encyclopedia
		The matrix algebra operations, in general, are not commutative and attention must be paid to whether the matrices are conformable with respect to the intended operation.
		However, on close scrutiny, matrix algebra operations of addition (of vectors, not elements of vectors, of matrices, not elements of matrices) can be used for concise expression of several key theorems of statistical theory and theory of probability.
		Note that the first matrix is a 2x3 matrix and the second matrix is a 3x2 matrix, the resulting matrix is a 2x2 matrix.
	en.wikipedia.org /wiki/Matrix_addition (470 words)

	Matrix addition - FreeEncyclopedia (Site not responding. Last check: 2007-10-08)
		The usual matrix addition is defined for two matrices of same dimensions.
		The sum of two m-by-n matrices A and B, denoted by A + B, is again an m-by-n matrix computed by adding corresponding elements, i.e., (A + B)[i, j] = A[i, j] + B[i, j].
		The m × n matrices with matrix addition as operation form an abelian group.
	openproxy.ath.cx /ma/Matrix_addition.html (205 words)

	MATRIX and VECTOR BASICS (Site not responding. Last check: 2007-10-08)
		A matrix is a rectangular array of elements arranged in rows and columns.
		A matrix is a rectangular array of elements, a set of vectors and geometrically a set of lines in p-space.
		Matrix rank, singularity status, invertability and linear dependency among columns and rows are all interrelated.
	ifasstat.ufl.edu /seminars/ifasstat/matrix/matrixa.htm (2175 words)

	EF 1574 Spring 2001 Project 4 (Site not responding. Last check: 2007-10-08)
		This project is a continuation of Project 4 (Matrix Operations) and is aimed at improving your understanding of classes and in appreciating their functionality.
		The number in the first line of the input text file is the row number of the matrix and the number in the second line is the column number of the matrix.
		The size of matrix A. The contents of matrix A. The size of matrix B. The contents of matrix B. The resultant matrix size and the operation performed.
	www.ee.vt.edu /~ef1574/projects/project5.html (1333 words)

	Matrix Operations
		This is a binary operator that performs matrix addition on the matrices "matrix1" and "matrix2", storing the result in a new matrix "temp-mat", "temp-mat" is then returned on exit.
		The matrix that is returned is an N by 1 matrix contaning the solution for each variable.
		All it does is take the i,jth element in the M by N matrix, and turns it into the j,ith element in the N by M matrix.
	www.gwydiondylan.org /gdref/gdlibs/libs-matrix-operations.html (578 words)

	Lab #2 : Modifying the Matrix Class (Site not responding. Last check: 2007-10-08)
		The lab is designed to give you experience with writing the matrix operations of addition, subtraction, and multiplication modifying the Matrix class that has properties that are two dimensional arrays to represent the matrices data.
		Matrix addition involves adding up the corresponding elements in two matrices to form their sum.
		The matrix which is the final product has the same number of rows as the first matrix in the product, and the same number of columns as the second matrix in the product.
	home.messiah.edu /~deroos/CSC182/Matrix (908 words)

	Arithmetic Operators (Site not responding. Last check: 2007-10-08)
		Addition of a scalar to all elements of a matrix.
		Subtraction of a scalar from all elements of a matrix.
		Unary operator, returns the negative of a matrix by subtracting all elements from zero.
	www.psatellite.com /products/html/matrixlib_api/a00018.html (343 words)

	Construct: Matrix Class Reference (Site not responding. Last check: 2007-10-08)
		Matrix (const double m00, const double m01, const double m02, const double m03, const double m10, const double m11, const double m12, const double m13, const double m20, const double m21, const double m22, const double m23, const double m30, const double m31, const double m32, const double m33)
		Creates a transformation matrix representing a scaling by the vector 's', the result's are stored in "this".
		The j position in the matrix to retrieve the data from.
	voronoi.sbp.ri.cmu.edu /software/Construct/doc/html/classMatrix.html (368 words)

	Matrix
		Matrices are treated as values wherever possible, so matrix operations such as multiplication produce a new matrix as the result, rather than operate directly on the matrix.
		As much of the matrix that can be copied will be copied, with excess parts being discarded, and remaining parts of the copy filled with a unit matrix.
		A new matrix which is the inverse of this matrix.
	www.charvolant.org /~doug/starmap/matrix/org/charvolant/matrix/Matrix.html (592 words)

	Matrix Transformations - 3DSoftware.com
		Matrix algebra is a part of linear algebra that is used extensively in computer graphics programming.
		Such a matrix, which has the same number of rows and columns, is called a square matrix.
		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.
	www.3dsoftware.com /Math/MatrixTransformations (1031 words)

	Matrix Operations for Image Processing
		One nice property of this saturation matrix is that the luminance of input RGB colors is maintained.
		This matrix can also be used to complement the colors in an image by specifying a saturation value of -1.0.
		Each color transformation is represented by a 4 by 4 matrix, similar to matrices commonly used to transform 3D geometry.
	www.sgi.com /misc/grafica/matrix (850 words)

	Matrix Operations
		The result is a new matrix with the same dimensions in which each element is the sum of the corresponding elements of the previous matrices.
		The inverse of a square matrix is a matrix of the same size that, when multiplied by the matrix, gives an identity matrix of the same size.
		Matrix inversion is often used to solve a set of simultaneous linear equations.
	www.stanford.edu /~wfsharpe/mia/mat/mia_mat2.htm (1904 words)

	Matrix Algebra (Site not responding. Last check: 2007-10-08)
		A diagonal matrix is a square matrix in which all the elements are zero except for the elements on the leading diagonal, eg:
		An orthogonal matrix is a square matrix which produces a unit matrix if it is multiplied by its own transpose.
		The determinant of a square matrix is a single number calculated by combining all the elements of the matrix.
	www.morello.co.uk /matrixalgebra.htm (1255 words)

	Matrix and matrix operations (Site not responding. Last check: 2007-10-08)
		A matrix is a rectangular array or table of numbers.
		Addition of two matrices A and B is possible only if the two matrices are equal.
		The matrix is initialized to an identity matrix, i.e.
	www.cs.fit.edu /wds/classes/cse5255/thesis/matrix/matrix.html (727 words)

	[No title]
		, is a square n x n matrix with a 1 on the main diagonal and a 0 elsewhere in the matrix.
		A block matrix is a matrix in which every entry is a matrix with fixed dimensions.
		An n x n circulant matrix C has the property the the entries on the kth row are a right cyclic shift by k-1 places of the entries on the first row.
	www.people.vcu.edu /~dprimeau/cmsc621/fall02/presentations/tyson/tyson62.html (1036 words)

	6.2 - Operations with Matrices
		The number of columns in the first matrix must be equal to the number of rows in the second matrix.
		Since the number of columns in the first matrix is equal to the number of rows in the second matrix, you can pair up entries.
		A matrix may be divided by a scalar.
	www.richland.edu /james/lecture/m116/matrices/operations.html (833 words)

	Addition of Vectors and Matrices
		The parallelogram rule implies that the addition of vectors is commutative.
		It's clear that if we define matrix addition again componentwise, the operation will be both associative and commutative.
		Because of this, some property of the addition of numbers are inherited by the addition of functions.
	www.cut-the-knot.com /do_you_know/add_vec.shtml (956 words)

	15.1.2 Matrix Operations: Sums and Products
		Addition of two matrices may arise when two sets of equations relate the same set of variables.
		The implementation of matrix addition is easy, and the code is shown in Figure 15.5.
		A good reference [1], for matrix computational methods as well as other numeric methods, is given at the end of this chapter.
	www-ee.eng.hawaii.edu /Courses/EE150/Book/chap15/subsection2.1.1.2.html (371 words)

	Matrix combinators in Joy
		Each element in the result matrix M3 is just the arithmetic sum of the corresponding elements of the other two matrices M1 and M2.
		In Joy a matrix of I rows and J columns can be represented as a list of I lists each of J elements.
		Comparing logical matrix multiplication and set matrix multiplication, the two are almost identical except for the different zero elements false and {}.
	www.latrobe.edu.au /philosophy/phimvt/joy/jp-matmul.html (3072 words)

	Matrices-Unit3-.html
		To define the operations of matrix addition and subtraction and state the
		To specify the laws obeyed by matrix addition and subtraction.
		matrix, which may be obtained using either of the following alternative methods.
	www.adeptscience.co.uk /products/mathsim/maple/powertools/linearalgebra/html/Matrices-Unit3-.html (526 words)

	Matrices
		The number of columns from the first matrix must be the same as the number of rows of the second matrix.
		A 3 by 4 matrix is not compatible with a 3 by 4 matrix.
		However it is compatible with any matrix with 4 rows like a 4 by 1, 4 by 3 and so on.
	www.projectgcse.co.uk /maths/matrices.htm (220 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		The numbers in a matrix are called elements or entries of the matrix.
		Matrix multiplication is a little more complicated, and will be shown in the next section.
		The transpose of a matrix A is denoted AT.
	www.math.sc.edu /~kidd/math170sec31.doc (658 words)

	What...is the matrix? (Site not responding. Last check: 2007-10-08)
		Addition and subtraction are inverses of each other, as are multiplication and division.
		Some properties which of matrix addition, which you should see, is that it is commutative and associative.
		We are going to start by looking at the simplest case of matrix multiplication: multiplying a matrix with the dimensions 1 x p and a matrix that is p x 1, which is pretty much the same as multiplying a row by a column.
	members.shaw.ca /mathematica/ahabTutorials/matrices.html (5479 words)

	Rules for Matrix Addition (Site not responding. Last check: 2007-10-08)
		Of course, the sum is the same as the non-zero matrix.
		You should be happy with the following rules of matrix addition.
		This is because ordinary addition is being done on the corresponding elements of the two matrices, and ordinary (real) addition is commutative:
	chortle.ccsu.ctstateu.edu /VectorLessons/vmch13/vmch13_9.html (116 words)

	[No title]
		A matrix with one row is called a row vector, and a matrix with one column is called a column vector.
		e.g.: ó¨Matrix scalar multiplication¨L Multiplication of a matrix or a vector by a scalar is also straightforward:ó¨Transpose of a matrix¨0 Taking the transpose of a matrix is similar to that of a vector: The diagonal elements in the matrix are unaffected, but the other elements are switched.
		To find the rank of a matrix by hand, use Gauss elimination and the linearly dependant row vectors will fall out, leaving only the linearly independent vectors, the number of which is the rank.
	www.eng.fsu.edu /~palanki/orient/lec1.ppt (1262 words)

	15.3 Matrix Addition, Multiplication and Multiplication by a Number (Site not responding. Last check: 2007-10-08)
		A matrix having only one row is called a row vector; a matrix having only one column is called a column vector.
		The transpose of a column vector is a row vector.
		The inverse of an n by n matrix A, is the matrix A
	www-math.mit.edu /~djk/18_022/chapter15/section03.html (502 words)

	CS 515 Assignment 1, Fall 2005 (Site not responding. Last check: 2007-10-08)
		From the abstract point of view, the values are 2-dimensional arrays of integers, and the operations you need to implement are matrix addition (+), matrix multiplication (), and matrix* transpose.
		Addition of two matrices A (ra x ca) and B (rb x cb) is defined only if A and B have the same dimensions, ie, if ra==rb and ca==cb, in which case the result has the same size.
		To transpose a matrix, you interchange the rows and columns.
	pubpages.unh.edu /~cs515/a1.html (678 words)

	Matrix Addition and Multiplication (Site not responding. Last check: 2007-10-08)
		Next: Faster Matrix Multiplication Algorithms Up: Matrix Operations Previous: Terms and Definitions
		Addition of two matrices is very simple: the sum of two matrices is the matrix composed of the sums of elements of the two matrices:
		The algorithm for multiplication is quite a bit different than might be expected- instead of simply multiplying the elements together, each element of the product is the result of several operations, as described in algorithm 4.2.
	www.eecs.harvard.edu /~ellard/Q-97/HTML/root/node18.html (133 words)

	Matrix Algebra (Site not responding. Last check: 2007-10-08)
		Given two matrices of the same size, that is, the two matrices have the same number of rows and columns, we define their sum by constructing a third matrix whose entries are the sum of the corresponding entries of the original two matrices.
		It is worth noting here that if the matrix A is an m by n matrix, then the first I symbolizes the n by n identity matrix, and the second I, the m by m identity matrix.
		The transpose of an m by n matrix, A, is an n by m matrix, and is obtained by writing the rows of A as the columns of its transpose.
	www.math.tamu.edu /~stecher/Linear-Algebra/Matrices/operations.html (404 words)

	Add Method
		A Matrix instance on the left side of the addition operator.
		A Matrix instance on the right side of the addition operator.
		A Matrix object that represents the result of the addition.
	www.bluebit.gr /NET/Library/Matrix-Add.html (235 words)

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