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Topic: Generalized permutation matrix

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Permutation matrix

Permutation matrix

	GNU Emacs Calc 2.02 Manual: Matrix Functions
		The matrix or vector is replaced by the specified row or element in the form of a vector or scalar, respectively.
		Matrix inverses are recorded so that once an inverse (or determinant) of a particular matrix has been computed, the inverse and determinant of the matrix can be recomputed quickly in the future.
		The first is a permutation matrix that arises from pivoting in the algorithm, the second is lower-triangular with ones on the diagonal, and the third is upper-triangular.
	www.xemacs.org /Documentation/packages/html/calc_12.html (8744 words)

	NationMaster - Encyclopedia: Permutation matrix
		corresponding to the permutation π=(1)(4 2 5 3) is
		In matrix theory, a generalized permutation matrix is a matrix with the same nonzero pattern as a permutation matrix, i.
		One theorem regarding the inverse permutation is the effect of a conjugation of a permutation by a permutation in a permutation group.
	www.nationmaster.com /encyclopedia/Permutation-matrix (1410 words)

	permutation matrix
		In linear algebra, a permutation matrix is a binary matrix that has exactly one 1 in each row or column and 0s elsewhere.
		The n-by-n permutation matrices form a group under matrix multiplication with the identity matrix as the identity element.
		corresponding to the permutation π=(1)(2 4 5 3) is
	www.abacci.com /wikipedia/topic.aspx?cur_title=permutation_matrix (646 words)

	Permutation matrix - Definition, explanation
		being the i-th vector in the identity matrix.
		A permutation matrix is a stochastic matrix; in fact doubly stochastic.
		corresponding to the permutation π=(1)(2 4 5 3) is
	www.calsky.com /lexikon/en/txt/p/pe/permutation_matrix.php (653 words)

	Permutation matrix - Encyclopedia, History, Geography and Biography
		In mathematics, in matrix theory, a permutation matrix is a (0,1)-matrix that has exactly one entry 1 in each row and each column and 0's elsewhere.
		1 and 2 and \ldots and j \\a_1 and a_2 and \ldots and a_j\end{bmatrix}is the permutation form of the permutation matrix.
		\begin{bmatrix} 5 and 0 and 0 and 0 and 0 \\0 and 3 and 2 and 0 and 0 \\0 and 0 and 0 and 5 and 0 \\0 and 1 and 2 and 0 and 2 \\0 and 1 and 1 and 0 and 3 \end{bmatrix}.This matrix is the sum of 5 permutation matrices.
	www.arikah.com /encyclopedia/Permutation_matrix (1047 words)

	Generalized permutation matrix
		In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e.
		The set of n×n generalized permutation matrices with entries in a field F forms a subgroup of the general linear group GL(n,F), in which the group of nonsingular diagonal matrices Δ(n, F) forms a normal subgroup.
		Monomial matrices occur in representation theory in the context of monomial representations.
	encycl.opentopia.com /term/Generalized_permutation_matrix (283 words)

	Permutation matrix - Glasgledius (Site not responding. Last check: )
		In linear algebra, a Permutation matrix is a matrix that has exactly one 1 in each row or column and 0s elsewhere.
		For example, the permutation matrix corresponding to σ=(1)(2 4 5 3) is
		In general, for a permutation σ on n objects, the correponding permutation matrix is an n-by-n matrix P
	www.glasglow.com /E2/pe/Permutation_matrix.html (120 words)

	List of matrices
		Companion matrix — a matrix whose eigenvalues are equal to the roots of the polynomial.
		Generator matrix — a matrix in coding theory whose rows generate all elements of a linear code.
		Polynomial matrix — a matrix with polynomials as its elements.
	www.1bx.com /en/List_of_matrices.htm (2391 words)

	Permutation matrix (Site not responding. Last check: )
		Permutation matrices are the matrix representation of permutation s.
		In general, for a permutation σ on ''n objects, the corresponding permutation matrix is an n -by- n matrix P
		A permutation matrix is a stochastic matrix ; in fact doubly stochastic.
	www.serebella.com /encyclopedia/article-Permutation_matrix.html (730 words)

	List of matrices - Gurupedia
		Companion matrix - the companion matrix of a polynomial is a special form of matrix, whose eigenvalues are equal to the roots of the polynomial.
		Generalized permutation matrix - a square matrix with precisely one nonzero element in each row and column.
		Toeplitz matrix - a matrix with constant diagonals.
	www.gurupedia.com /l/li/list_of_matrices.htm (608 words)

	List of matrices (Site not responding. Last check: )
		Nonnegative matrix — a matrix with all nonnegative entries.
		Rotation matrix — a matrix representing a rotational geometric transformation.
		Toeplitz matrix — a matrix with constant diagonals.
	www.wozhidao.org /en/List_of_matrices.htm (2391 words)

	NationMaster - Encyclopedia: Monomial
		In linear algebra, a diagonal matrix is a square matrix in which the entries outside the main diagonal are all zero.
		In mathematics, and in particular group representation theory, the induced representation is one of the major general operations for passing from a representation of a subgroup H to a representation of the (whole) group G itself.
		Obviously, a monomial matrix is a square matrix and there exists a rearrangement of rows and columns such that the result is a diagonal matrix.
	www.nationmaster.com /encyclopedia/Monomial (1277 words)

	Permutation matrix . Generalized permutation matrix . Group_(mathematics) . (0,1)-matrix
		-matrix binary matrix that has exactly one entry 1 in each row and each column and 0s elsewhere.
		You can perform division in groups; that is, given elements a and b of the group G, there is exactly one solution x in G to the equation x a = b and exactly...
		mathematics matrix whose entries are all either zero or one.
	www.uk.kunsimuna.net /Permutation_matrix_UK_195911_dl (499 words)

	wikien.info: Main_Page (Site not responding. Last check: )
		One can show that every doubly stochastic matrix is a convex combination of permutation matrices of the same size, giving permutation matrices a characterisation as the set of extreme points.
		where [\Lambda] is a diagonal matrix of eigenvalues and [Q] is the matrix of eigenvectors.
		a_1 & a_2 & \ldots & a_j\end] is the permutation form of the permutation matrix.
	www.hostingciamca.com /index.php?title=Permutation_matrix (1092 words)

	Basic Matrix Functions - Untitled
		Rows/columns of a (and b) that are isolated by permutation are not scaled.
		The eigenvalues (and eigenvectors) of a matrix are computed in a several step process which begins with a Hessenberg decomposition, followed by a Schur decomposition, from which the eigenvalues are apparent.
		Incorrectly defining the matrix type will result in incorrect results from solutions of linear equations, and so it is entirely the responsibility of the user to correctly indentify the matrix type.
	www.gnu.org /software/octave/doc/interpreter/Basic-Matrix-Functions.html (575 words)

	Permutation matrix (Site not responding. Last check: )
		In linear algebra, a permutation matrix is a binary matrix that has exactly one 1 in each row or column and 0selsewhere.
		Now, in performing matrix multiplication, one essentially forms the dot product of each row of the first matrix with each eachcolumn of the second.
		A possible generalization ofpermutation matrices are matrices where the values of each column and row add up to a number c.
	www.therfcc.org /permutation-matrix-242107.html (411 words)

	Sparse Matrix Ordering Example
		Graph theory was identified as a powerful tool for sparse matrix computation when Seymour Parter used undirected graphs to model symmetric Gaussian elimination more than 30 years ago [28].
		Because the choice of permutation P will directly determine the number of fill-in elements (elements present in the non-zero structure of L that are not present in the non-zero structure of A), the ordering has a significant impact on the memory and computational requirements for the latter stages.
		However, unstructured meshes generated by FEM does not provide an obvious labeling (numbering) of the unknowns while it is vital to have it for matrix-vector notation of the underlying algebraic equations.
	www.boost.org /libs/graph/doc/sparse_matrix_ordering.html (1346 words)

	math lessons - Generalized permutation matrix
		where D is a nonsingular diagonal matrix and P is a permutation matrix.
		The set of n×n generalized permutation matrices with entries in a field F forms a subgroup of the general linear group GL(n,F) in which the group of diagonal matrices is a normal subgroup.
		Generalized permutation matrices occur in representation theory in the context of monomial representations.
	www.mathdaily.com /lessons/Generalized_permutation_matrix (214 words)

	Bambooweb: List of matrices
		Gramian matrix - a real symmetric matrix that can be used to test for linear independence of any functions.
		Permutation matrix - matrix representation of a permutation.
		Transition matrix - a matrix representing the probabilities of changing from one state to another
	www.bambooweb.com /articles/L/i/List_of_matrices.html (642 words)

	THE PERRON-FROBENIUS THEOREM
		Suppose A is the transition matrix of a Markov chain.
		An nxn nonnegative matrix A is primitive iff A
		if the matrix is irreducible but not primitive then the greatest common divisor of the lengths of all cycles is the same as the number of eigenvalues with magnitude the same as the dominant eigenvalue (and including it).
	www.prenhall.com /divisions/esm/app/ph-linear/leon/html/perron.html (2166 words)

	Generalized permutation matrix (Site not responding. Last check: )
		In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e.
		The set of n×n generalized permutation matrices with entries in a field F forms a subgroup of the general linear group GL(n,F), in which the group of nonsingular diagonal matrices Δ(n, F) forms a normal subgroup.
		Monomial matrices occur in representation theory in the context of monomial representations.
	www.omniknow.com /common/wiki.php?in=en&term=Generalized_permutation_matrix (1512 words)

	Linear Algebra Glossary
		The inverse of a (nonsingular) circulant matrix is a circulant matrix.
		The transpose of a circulant matrix is a circulant matrix.
		The cofactor matrix of a square matrix A is generally used to define the adjoint matrix, or to represent the determinant.
	orion.math.iastate.edu /burkardt/papers/linear_glossary.html (13535 words)

	ICALAB FAQ
		However, please note that for very long recordings the mixing matrix may change in time and a linear model with a fixed mixing matrix will not be valid, thus in such case it is necessary to divide data into smaller blocks.
		matrix is a generalized permutation matrix (or in some sense very close to it) then both algorithms estimate the same mixing (or separating) matrix and, consequently, they estimate the same components.
		More generally, an optimal local ICA can be implemented as the result of mutual interaction of two processes: A suitable clustering (or splitting) process and the application of the ICA process to each such cluster.
	www.bsp.brain.riken.jp /ICALAB/faq/faq.html (4922 words)

	JAMA: Java Matrix Package
		JAMA is based on a single matrix class within a strictly object-oriented framework.
		Five fundamental matrix decompositions, which consist of pairs or triples of matrices, permutation vectors, and the like, produce results in five decomposition classes.
		These decompositions are accessed by the Matrix class to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions.
	math.nist.gov /javanumerics/jama (876 words)

	Generalized permutation matrix - Term Explanation on IndexSuche.Com (Site not responding. Last check: )
		is a matrix with the same nonzero pattern as a permutation_matrix, i.e.
		An example of generalized permutation_matrix is :\begin{bmatrix}0 & 0 & 3 & 0\\ 0 & -2 & 0 & 0\\ 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 \end{bmatrix} An interesting theorem states the following: : If a nonsingular matrix and its inverse are both nonnegative matrices (i.e.
		matrices with nonnegative entries), then the matrix is a generalized permutation_matrix.
	www.indexsuche.com /Generalized_permutation_matrix.html (139 words)

	Linear Algebra Glossary
		The inverse of a (nonsingular) circulant matrix is a circulant matrix.
		The transpose of a circulant matrix is a circulant matrix.
		The cofactor matrix of a square matrix A is generally used to define the adjoint matrix, or to represent the determinant.
	www.math.iastate.edu /burkardt/papers/linear_glossary.html (13535 words)

	[No title] (Site not responding. Last check: )
		In matrix theory, a generalized permutation matrix is a matrix with the same nonzero pattern as a
		If a nonsingular matrix and its inverse are both nonnegative matrices (i.e.
		matrices with nonnegative entries), then the matrix is a generalized permutation matrix.
	www.en-cyclopedia.com /wiki/Generalized_permutation_matrix (53 words)

	Definition of permutation (album)
		''permutation'' and a [[set]]: the elements of a permutation are arranged in a specified order.
		8: the permutation matrix ''P''_andpi; with ''m'' elements i...
		of permutation in music is the same as that of [[permutation]] in [[combinatoricscombinatorial]] [[mathematic...
	www.wordiq.com /search/permutation+%28album%29.html (866 words)

	linalg
		It may be used to solve, symmetric, nonsymmetric, standard or generalized eigenvalue problems, and to compute a partial singular value decomposition.
		The decomposition, (guptri - generalized upper triangular form) is a generalization, of the Schur canonical form of A -zI to matrix pencils and reveals, the Kronecker structure of a singular pencil.
		Damped least squares -- solve (A)x = (b), dampI) (0, in the least-squares sense, where A is a matrix with m rows and n columns, b is an, m-vector, and damp is a scalar.
	www.netlib.org /linalg (1490 words)

	Permutation matrix - The Jiggies Reference Guide (Site not responding. Last check: )
		In general, for a permutation σ on n objects, the corresponding permutation matrix is an n-by-n matrix P
		1 & 2 & \ldots & j \\ a_1 & a_2 & \ldots & a_j\end{bmatrix} is the permutation form of the permutation matrix.
		1 & 2 & \ldots & j \\ a_1 & a_2 & \ldots & a_j\end{bmatrix} So, permutaton matrices do indeed permute the order of elements in vectors multiplied with them.
	www.jiggies.com /reference/Permutation_matrix (367 words)

	Linear Algebra Glossary
		The vector (1,1,...,1) is an eigenvector of the matrix, with eigenvalue equal to the row sum.
		The matrix is assumed to be symmetric positive definite; if it is also large and sparse, a suitable preconditioner may be the Incomplete Cholesky Factorization.
		Moreover, in the general case, the principal axes are pairwise orthogonal vectors, and in the degenerate case, may be chosen pairwise orthogonal.
	people.scs.fsu.edu /~burkardt/html/linear_glossary.html (11910 words)

	[No title]
		One can show that every doubly stochastic matrix is a
		convex linear combination of permutation matrices of the same size, giving permutation matrices a characterisation as the set of extreme points.
		group under matrix multiplication with the identity matrix as the
	www.en-cyclopedia.com /wiki/Permutation_matrix (431 words)

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