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Topic: Symmetric matrix

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List of matrices

Diagonal matrix

Hermitian matrix

Matrix (mathematics)

Inverse matrix

Transpose

Toeplitz matrix

Normal matrix

Orthogonal matrix

Matrix inversion

Stochastic matrix

Unitary matrix

Matrix multiplication

Identity matrix

Singular value decomposition

	Symmetric Matrix
		Assigns a matrix expression to the symmetric matrix.
		Subtracts the matrix expression from the symmetric matrix.
		Subtracts the matrix expression from the symmetric adaptor.
	www.boost.org /libs/numeric/ublas/doc/symmetric.htm (338 words)

	Bluebit .NET Matrix Library 2.5 Documentation
		Represents a matrix having complex floating point numbers as elements.
		Thrown when a non-square matrix is passed as a parameter to a method that expects a square matrix.
		Thrown when a matrix has found to be singular not allowing the successful completion of a method.
	www.bluebit.gr /NET/Library (674 words)

	Data-matrix Software
		This Matrix Clock will refer to your fond memories of The Matrix movie and will inspire you to Neo's daring to be free from the matrix, to Trinity's intensity of Love, to firm and passionate leadership of Nebuchadnezzar ship commander Morpheus.
		Matrix Screensaver simulates the green falling code from the Matrix movie..
		NMath Matrix is an advanced matrix manipulation library that extends the general matrix classes of NMath Core to include structured sparse matrix classes and factorizations, general matrix decompositions, advanced least squares solutions, and solutions to eigenvalue problems.
	www.programurl.com /software/data-matrix.htm (991 words)

	PlanetMath: skew-symmetric matrix
		According to Jacobi's Theorem, the determinant of a skew-symmetric matrix of odd order is zero.
		Cross-references: odd, determinant, Jacobi's theorem, imaginary, eigenvalues, vector space, operator, trace, transpose, properties, skew-Hermitian matrices, complex, implies, skew-symmetric, matrix, real, order, square matrix
		This is version 6 of skew-symmetric matrix, born on 2001-11-21, modified 2006-07-05.
	planetmath.org /encyclopedia/SkewSymmetricMatrix.html (128 words)

	Special Matrices: Triangular, Symmetric, Diagonal
		We have seen that a matrix is a block of entries or two dimensional data.
		A symmetric matrix is a matrix equal to its transpose.
		A diagonal matrix is a symmetric matrix with all of its entries equal to zero except may be the ones on the diagonal.
	www.sosmath.com /matrix/matrix3/matrix3.html (345 words)

	Matrix Fundamentals
		A matrix is denoted by a capital letter; its elements are denoted by the same lower case letter with row/column subscripts.
		The elements in a square matrix that have same row index and column index are called the diagonal elements of the matrix, or simply the diagonal of the matrix.
		The transpose and Hermitian transpose of a matrix A are denoted by A
	www.intel.com /software/products/mkl/docs/WebHelp/mthapa4.html (579 words)

	Matrix Algebra
		Elements (entries) of the matrix are referred to by the name of the matrix in lower case with a given row and column (again, row comes first).
		(The main or principal diagonal in matrix B is composed of elements all equal to 1.) With a square, symmetric matrix, the transpose of the matrix is the original matrix.
		Multiplying a matrix by the identity matrix is analogous to the real number operation of multiplying a number or variable by 1: the resulting output is identical to the numbers input.
	luna.cas.usf.edu /~mbrannic/files/regression/matalg.html (1775 words)

	Matrix Reference Manual: Special Matrices
		A 3#3 orthogonal matrix is either a rotation matrix or else a rotation matrix plus a reflection in the plane of the rotation according to whether it is proper or improper.
		A Rotation matrix is orthogonal with a determinant of +1.
		A signature matrix is a diagonal matrix whose diagonal entries are all +1 or -1.
	www.ee.ic.ac.uk /hp/staff/dmb/matrix/special.html (4464 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)

	3.3 Matrix Precision and Shape
		A symmetric matrix is a square matrix with the property that the matrix is equal to its transpose.
		Symmetric matrices are often used to represent quadratic forms; for example, the energy in a system can be represented as a symmetric matrix.
		A symmetric matrix is a special case of a Hermitian matrix where all the elements are real.
	www.roguewave.com /support/docs/hppdocs/lpkug/3-3.html (659 words)

	Matrix Market: Glossary
		A matrix is diagonally dominant if the absolute value of each diagonal element is greater than the sum of the absolute values of the other elements in its row (or column).
		A Hessenberg matrix is `almost' triangular, that is, it is (upper or lower) triangular with one additional off-diagonal band (immediately adjacent to the main diagonal).
		A symmetric matrix can always be reduced to a symmetric tridiagonal form by a finite sequence of similarity transformations.
	math.nist.gov /MatrixMarket/glossary.html (756 words)

	Symmetric Matrices (Site not responding. Last check: )
		The transpose of a matrix is matrix formed by exchanging the rows and columns of a matrix (i.e.
		A symmetric matrix is one where every element in the transpose of the matrix has the same value as the original matrix.
		The input format for each matrix will consist of two values indicating the number of rows and columns in the matrix followed by one line for each row containing the elements for each column in that row.
	www.cs.umd.edu /Outreach/hsContest97/questions/node2.html (219 words)

	Matrix Manual: Special Matrices
		matrix, A, is an nn Toeplitz matrix* in which a(i,j) is a function of {(i-j) modulo n}.
		A is symmetric iff it is congruent to a diagonal matrix.
		Any square matrix may be uniquely decomposed as the sum of a symmetric matrix and a skew-symmetric matrix.
	www.psi.toronto.edu /matrix/special.html (2192 words)

	ISU Combinatorial Matrix Theory Research Group
		For a positionally symmetric pattern Q, the pattern-graph of Q is the graph having {1,...,n} as its vertex set and, as its set of edges, the set of (unordered) pairs {i,j} such that position (i,j) (and therefore also (j,i)) is in Q. Matrix Completions Problems for Patterns Homepage
		In recent years there has been a great deal of interest in the possible eigenvalues of a real symmetric matrix whose nonzero entries are described by a given graph or by the pattern of the signs of the entries, especially a tree (i.e., a connected graph with no cycles).
		A Fischer matrix is a P-matrix that satisfies Fischer's inequality for all principal submatrices.
	orion.math.iastate.edu /lhogben/research/mcgrg.html (1417 words)

	Matrix Algebra
		Symmetric matrices are used in the method of linear least squares (see App.
		Important properties of the transpose operation and triangular and symmetric matrices are contained in Theorem 1.5.3.
		The power of a square matrix, which is important in the subject of Markov chains (which we mentioned briefly in Sec.
	distance-ed.math.tamu.edu /Math640/chapter1/node8.html (1646 words)

	Some Properties of Symmetric Indefinite Matrix Pairs
		is purely an algebraic property and is not sufficient to ensure any of the special mathematical properties enjoyed by a definite matrix pencil, such as those discussed in §2.3.
		The eigenvalues of a definite matrix pencil are all real, but an indefinite pencil may have complex eigenvalues.
		A further distinction from the definite case is that an indefinite matrix pencil may not have a complete set of eigenvectors.
	www.cs.utk.edu /~dongarra/etemplates/node297.html (388 words)

	JSpline+ API Specification: Package ru.sscc.matrix.solve
		The matrix to be used in SLAE is attached to the solver.
		When the matrix is factorized, it becomes non-algebraic, and all algebraic operations with it are blocked.
		While a matrix is factorized, the reduction accuracy level affects on the decision on columns dependency and on the constructing of matrix null space.
	www.excelsior-usa.com /doc/jspline/api/ru/sscc/matrix/solve/package-summary.html (1231 words)

	CenterSpace API Documentation - CenterSpace.NMath.Matrix
		A banded matrix is a matrix that has all its non-zero entries near the diagonal.
		A tridiagonal matrix is a matrix which has all its non-zero entries on the main diagonal, the super diagonal, and the subdiagonal.
		A symmetric banded matrix is a symmetric matrix that has all its non-zero entries near the diagonal.
	www.centerspace.net /doc/NMath/Matrix/ref (1869 words)

	symmetric matrix definition - Dictionary - MSN Encarta
		symmetric matrix definition - Dictionary - MSN Encarta
		Search for "symmetric matrix" in all of MSN Encarta
		matrix symmetrical about diagonal: a square matrix that is identical to the matrix formed by transposing its rows and columns
	encarta.msn.com /dictionary_1861717674/symmetric_matrix.html (91 words)

	symmetric - Definitions from Dictionary.com
		noting a square matrix that is equal to its transpose.
		The relation a = b is symmetric, whereas the relation a > b is not.
		In linear algebra, a member of the tensor product of a vector space with itself one or more times, is symmetric if it is a fixed point of all of the linear isomorphisms of the tensor product generated by permutations of the ordering of the copies of the vector space as factors.
	dictionary.reference.com /browse/symmetric (488 words)

	OLS :: Open Learning Support
		A non-symmetric n by n matrix of full rank (with indepedent columns) does not in general have a full rank n by n matrix of eigenvectors.
		The resulting diagonal matrix of your example only has orthogonal columns in the sense that they are in the same directions as the basis of eigenvectors.
		S is the matrix of orthonormal eigenvectors, L is the diagonal matrix of eigenvalues.
	mit.ols.usu.edu /courses/showthread?ForumID=6&RootPostID=902 (461 words)

	Covariance and Correlation
		Due to the symmetry property of covariances, this is necessarily a symmetric matrix.
		Cholesky matrix A lower-triangular matrix that acts as a matrix "square root" for a positive definite matrix.
		positive definite matrix A real symmetric matrix, all of whose eigenvalues are real and positive.
	www.riskglossary.com /articles/correlation.htm (348 words)

	Calculating the Square Root of a Matrix
		In analogy to the square root of a number, this matrix B is called the square root of the matrix A.
		The first matrix is the result: the square root of the original matrix.
		The result is emitted as the second matrix, which is indeed identical to the original one.
	seehuhn.de /comp/matrixfn (852 words)

	Manipulation of Triangular and Symmetric Matrices
		symmetric matrix is taken to be stored in the packed form with M(M+1)/2 elements.
		These are also stored in the packed form with all the zeros dropped; therefore, care has to be taken in the interpretation of a packed matrix as to whether it represents a symmetric or lower triangular array.
		(the inverse of a lower triangular matrix is lower triangular).
	wwwasdoc.web.cern.ch /wwwasdoc/shortwrupsdir/f112/top.html (230 words)

	Symmetric Matrices
		In this discussion, we will look at symmetric matrices and see that diagonalizing is a pleasure.
		This says that a symmetric matrix with distinct roots is always similar to a diagonal matrix.
		symmetric matrix, then any two eigenvectors that come from distinct eigenvalues are orthogonal.
	www.ltcconline.net /greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm (232 words)

	MATRIX
		Operations on matrices are specified in matrix equations preceded by the word MAT; these equations are just like the variable transformations performed by GENR, except for two things: they do not operate under control of the current SMPL and the results are stored as a matrix.
		These situations include, but are not limited to, the cross-product operation (which generates a symmetric matrix) and the calculation of a quadratic form (the expression ABA').
		They may be used anywhere in a MAT statement where scalars are allowed, keeping in mind that a scalar is also a 1 by 1 matrix.
	www.tspintl.com /products/tsphelp/matrix.htm (575 words)

	Diagonalizing Quaternion For 3x3 Symmetric Matrix (Site not responding. Last check: )
		Diagonalizing a symmetric 3x3 has various useful applications such as diagonalizing inertia tensors, fitting OBBs, finding principal axes, etc. The diagonal entries of the diagonalized matrix are the eigenvalues and the quaternion represents the eigenvectors in that the rows of the corresponding matrix are the eigenvectors.
		When you call the routine for a matrix M and get a quaternion q whose corresponding matrix is Q and then compute D=QMQ^T you will probably notice that the off diagonal elements of D are not quite zero.
		The algebra to derive all this is a bit trickier since you have the matrices on both sides (the diagonalizer and its inverse).
	www.melax.com /diag (602 words)

	Introduction to Econometrics - Matrix Algebra
		A special diagonal matrix is a matrix where all diagonal elements are equal to one (identity matrix denoted I).
		In our discussions we'll also always assume that these idempotent matrices are symmetric (which means that the element of the i-th row and the j-th column is equal to the element of the j-th row and the i-th column).
		The number of roots of a symmetric matrix A that are different from zero is equal to the rank of A.
	www.xycoon.com /matrix_algebra.htm (2244 words)

	Microsoft Excel Tutorials
		Tutorial on how to use Inverse matrix and matrix multiplication in MS Excel.
		Using MS excel Goal seek to find eigen value of a symmetric matrix.
		Learn simple matrix theory on how to obtain symmetric matrix from any matrix.
	people.revoledu.com /kardi/tutorial/Excel (491 words)

	WWW interactive mathematics server
		Matrix dialog, ask questions to get information in order to solve problems on matrices.
		Symmetric split, write a given matrix as sum of symmetric and antisymmetric matrices.
		Matrix multiplier, input two matrices and get their product (or other formula).
	webwork.math.ohio-state.edu /wims/wims.cgi (4774 words)

	Site map
		Reduction of a square matrix to upper Hessenberg form
		Reduction of a symmetric matrix to tridiagonal form
		Reduction of a Hermitian matrix to real tridiagonal form by the orthogonal similarity transformation.
	www.alglib.net /sitemap.php (153 words)

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