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	PlanetMath: matrix p-norm
		See Also: matrix norm, vector norm, Frobenius matrix norm
		Cross-references: Frobenius matrix norm, estimates, inequalities, eigenvalue, square root, calculate, norms, vector, definition, matrix, matrix norms, class
		This is version 10 of matrix p-norm, born on 2001-10-06, modified 2006-01-24.
	planetmath.org /encyclopedia/MatrixPnorm.html (160 words)

	NationMaster - Encyclopedia: Norm (mathematics)
		In linear algebra, functional analysis and related areas of mathematics, a norm is a function which assigns a positive length or size to all vectors in a vector space, other than the zero vector.
		Main article maximum norm In mathematical analysis, the uniform norm assigns to real- or complex-valued functions f the nonnegative number This norm is also called the supremum norm or the Chebyshev norm.
		is a rhomboid, for the 2-norm (Euclidean norm) it is the well-known unit circle, while for the infinity norm it is a square.
	www.nationmaster.com /encyclopedia/Norm-%28mathematics%29 (2519 words)

	Matrix Reference Manual: Matrix Properties
		The characteristic polynomial, p(t), of a matrix A
		The determinant of an orthogonal matrix is ±1.
		The determinant of a permutation matrix equals the signature of the column permutation.
	www.ee.ic.ac.uk /hp/staff/dmb/matrix/property.html (2541 words)

	Norm - Biocrawler (Site not responding. Last check: 2007-10-26)
		For philosophy, semantics and law, see norm (philosophy), which is a sentence or a meaning unit.
		The reduced norm in the theory of algebras.
		Norm Peterson is a character in the sitcom Cheers, and a spin-off, Norm.
	www.biocrawler.com /encyclopedia/Norms (199 words)

	Matrix norm
		We use term "vector norm" for the first definition and "matrix norm" for the second definition.
		is the Euclidean norm, then the induced matrix norm is the spectral norm.
		Spectral norm is the only minimal matrix norm which is an induced norm.
	www.xasa.com /wiki/en/wikipedia/m/ma/matrix_norm.html (335 words)

	PlanetMath: matrix norm
		A matrix norm is a norm on the set
		A vector norm is a matrix norm for which the ring
		This is version 7 of matrix norm, born on 2001-10-06, modified 2006-07-24.
	www.planetmath.org /encyclopedia/MatrixNorm.html (70 words)

	17.2 ELL_Matrix Methods
		A frequently used matrix norm is the Frobenius norm:
		The general class of matrix norms known as the p-norms are defined in terms of vector norms by:
		Calculating the 2-norm of a matrix requires an iterative procedure, and is not currently done in C
	www.lanl.gov /Caesar/node293.html (164 words)

	PlanetMath: Frobenius matrix norm
		function or Euclidean matrix norm is the norm function
		A nice property of the norm is that
		This is version 14 of Frobenius matrix norm, born on 2001-10-06, modified 2006-10-04.
	www.planetmath.org /encyclopedia/EuclideanMatrixNorm.html (130 words)

	The story of the rise of industry leading firm Norm Civata Co. with CANIAS ERP.
		Norm Civata Co. was founded in 1973 to prevent Turkey's dependency on foreign sources in the field of fastening components and has now become the industry leader, supplying 70 % of the total bolt and fastener production in Turkey today.
		Norm Civata Co. is the largest fastening components firm in Turkey, supplying 70% of general production.
		From a client perspective, it is possible to analyze Norm Civata Co. in 3 segments.
	www.canias.com /enterprise/news/20060626-norm-civata.html (1882 words)

	Matrix Group International, Inc. \| Web Design
		At Matrix, design projects reach far beyond the norm.
		At Matrix, we believe three designers are better than one.
		If we happen to be creating a content management system for your organization, the design templates used to publish content dynamically will comply with our overall design standards.
	www.matrixgroup.net /services/index.cfm?fa=design (555 words)

	Matrix Norm and Rank One Decomposition
		The three non-zero singular values tell you that the matrix has rank 3.
		But the value 0.01 is so small that A is nearly a rank two matrix.
		In fact the matrix B was created by setting that last singular value to zero.
	www.uwlax.edu /faculty/will/svd/norm/index.html (384 words)

	Matrix norm (Site not responding. Last check: 2007-10-26)
		The spectral norm of a Matrix A is the largest singular value of A or the square root of the largest eigenvalue of the positive-definite matrix AA
		For k=2, it corresponds to the Euclidean norm and is called the Frobenius norm.
		Frobenius norm is submultiplicative and is very useful numerical linear algebra.
	matrix-norm.borgfind.com (413 words)

	Krugle Code Search: matrix.c
		A matrix is assumed to be declared as double *, and it is allocated by MatrixAlloc.
		A row in the * matrix is (a_i, d_i, c_i), [2, pp.
		The n vectors are collected in a matrix, and the matrix is * both input and output.
	www.krugle.com /files/cvs/cvs.sourceforge.net/pdl/PDL/Basic/MatrixOps/matrix.c (706 words)

	The Finite Element Method (Partial Differential Equation Toolbox)
		Note that in the most common case, when the function d(x) is positive, the mass matrix M is positive definite symmetric.
		Some of the eigenvalues of this Hessenberg matrix Hj,j eventually give good approximations to the eigenvalues of the original pencil (K,M) when the basis grows in dimension j, and less and less of the eigenvector is hidden in the residual matrix Ej.
		It is not necessary to actually compute the eigenvector approximation yi to get the norm of the residual; we only need to examine the short vectors si, and flag those with tiny last components as converged.
	www.technion.ac.il /guides/matlab/toolbox/pde/4fem6.html (1090 words)

	Norm - Definition, explanation
		A map which assigns a length to vectorss, see norm (mathematics), normed vector space.
		The reduced norm in the theory of algebrass.
		NORM group coordinators in their areas who are on...
	www.calsky.com /lexikon/en/txt/n/no/norm.php (461 words)

	Matrix norm
		A matrix norm is a norm on the vector space of all real or complex m-by-n matrices.
		These norms are used to measure the "sizes" of matrices, and allow to talk about limits of sequences and infinite series of matrices.
		) is an m-by-n matrix with entries from the field K (which is either R or C).
	www.fastload.org /ma/Matrix_norm.html (292 words)

	Parallel Engineering and Scientific Subroutine Library for AIX Version 2 Release 3: Guide and Reference - PDLANGE and ... (Site not responding. Last check: 2007-10-26)
		is the row index of the global matrix A, identifying the first row of the submatrix A.
		is the column index of the global matrix A, identifying the first column of the submatrix A.
		This example computes the one norm of a complex general matrix A of order 9, using a 2 × 2 process grid.
	www.gwdg.de /service/rechenanlagen/parallelrechner/p690_documentation/pessl/html/pessl152.html (803 words)

	Testing Rank Deficiency in the Approximate Covariance Matrix (Site not responding. Last check: 2007-10-26)
		The inverse of the information matrix (or approximate Hessian matrix) is used for the covariance matrix of the parameter estimates, which is needed for the computation of approximate standard errors and modification indices.
		The numerical condition of the information matrix (computed as the crossproduct J'J of the Jacobian matrix J) can be very poor in many practical applications, especially for the analysis of unscaled covariance data.
		If no rank loss is detected, the inverse of the information matrix is used for the covariance matrix of parameter estimates, and the next two steps are skipped.
	www.sfu.ca /sasdoc/sashtml/stat/chap19/sect32.htm (320 words)

	frobenius norm
		Hi I'm in the process of proving a matrix norm.
		i think hurkyl is assuming you meant the euclidean norm, and then your formula would simply be the norm of a vector in euclidean n space.
		the properties of this norm are probably based on some inequality they teach at the beginnig of many courses called the schwartz inequality (see chapter 0 or 1 of spivak's calculus book).
	www.physicsforums.com /showthread.php?t=35511&goto=nextnewest (279 words)

	Dr. Dobb's \| Making the Tough Coding Decisions \| December 4, 2006
		This is the norm, or absolute value, of a vector.
		If you draw a vector in three (or more) dimensions, its norm is the same as the scalar length, as measured along the vector itself.
		For non-zero norms, the direction is well defined: the unitized vector should be parallel with the original vector.
	www.ddj.com /196601401?_requestid=641728 (2460 words)

	MIMS EPrints - 2006.160: Experience with a Matrix Norm Estimator
		Fortran 77 codes for estimating the 1-norm of a real or complex matrix were presented by Higham in [ACM Trans.
		Further observations about the norm estimation algorithm and experience in using it are reported here.
		In particular, an example is given where the algorithm requires nearly the maximum possible number of iterations.
	eprints.ma.man.ac.uk /339 (137 words)

	Banach algebra - Definition, explanation
		A Banach algebra is called "unital" if it has an identity element for the multiplication whose norm is 1, and "commutative" if its multiplication is commutative.
		The algebra of all bounded real- or complex-valued functions defined on some set (with pointwise multiplication and the supremum norm) is a unital Banach algebra.
		The algebra of all continuous linear operators on a Banach space E (with functional composition as multiplication and the operator norm as norm) is a unital Banach algebra.
	www.calsky.com /lexikon/en/txt/b/ba/banach_algebra.php (709 words)

	MP Forumsuche: matrix norm (Matroids Matheplanet) (Site not responding. Last check: 2007-10-26)
		Gegeben sei eine Matrix A. Diese ist orthogonal.
		Eine Matrix A ist genau dann normal, wenn A eine orthonormale Basis aus Eigenvektoren besitzt.
		gesucht: idempotente Matrix, deren Normquadrat nicht ganzzahlig ist
	www.matheplanet.com /matheplanet/nuke/html/searchbb.php?term=matrix+norm&forum=all&odirection=desc&sortby=t.topic_title (971 words)

	inv (MATLAB Functions)
		In practice, it is seldom necessary to form the explicit inverse of a matrix.
		Here is an example demonstrating the difference between solving a linear system by inverting the matrix with
		But the size of the residuals, obtained by plugging the computed solution back into the original equations, differs by several orders of magnitude.
	www.weizmann.ac.il /matlab/techdoc/ref/inv.html (306 words)

	Matematicamente.it :: Leggi argomento - Norma naturale di matrice
		fra l'altro le norme su uno spazio di dimensione finita sono tutte equivalenti...
		Infatti le norme servono per fare i limiti, per la continuità eccetera..
		norm is called the spectral norm and is the square root of the largest
	www.matematicamente.it /f/viewtopic.php?t=13210 (879 words)

	Math Forum Discussions
		not induced by, or compatible with in other terminology, a vector norm.
		One description is that it treats the matrix as if it were a vector rather
		the norm of A as an operator from R^n to R^n with the usual
	www.mathforum.com /kb/message.jspa?messageID=4876182&tstart=0 (199 words)

	Norm Thompson Resources & Information - norm thompson catalog
		Look up norm on Wiktionary, norm thompson women's sandals the free dictionary.
		Norm (mathematics), a map which assigns a length to vectors
		Norm Peterson, a character in the sitcom norm thompson catalog coupon Cheers and norm thompson outfitters sheepskin shop its spin-off Norm
	www.bizhisto.com /Biz-Retail-Companies-N---O/Norm-Thompson.html (156 words)

	Pascal's Wager (Stanford Encyclopedia of Philosophy)
		It is typical to present these numbers in a decision matrix, with the columns corresponding to the various relevant states of the world, and the rows corresponding to the various possible actions that the agent can perform.
		We can think of Pascal's Wager as having three premises: the first concerns the decision matrix of rewards, the second concerns the probability that you should give to God's existence, and the third is a maxim about rational decision-making.
		All that we have granted is that one norm — the norm of rationality — prescribes wagering for God.
	plato.stanford.edu /entries/pascal-wager (5547 words)

	DLANGE(l) (Site not responding. Last check: 2007-10-26)
		ARGUMENTS NORM (input) CHARACTER*1 Specifies the value to be returned in DLANGE as described above.
		M (input) INTEGER The number of rows of the matrix A. When M = 0, DLANGE is set to zero.
		N (input) INTEGER The number of columns of the matrix A. When N = 0, DLANGE is set to zero.
	www.uwm.edu /cgi-bin/Dept/IMT/wwwman?topic=DLANGE(3lapack)&msection=3 (110 words)

	Math Forum Discussions
		a matrix with the diagonal elements the eigenvalues of the matrix
		On the other hand, this (the spectral radius) is not a "norm" of a matrix.
		can not be zero when the matrix is not zero.
	www.mathforum.org /kb/message.jspa?messageID=267948&tstart=0 (402 words)

	Banach algebra (Site not responding. Last check: 2007-10-26)
		The algebra multiplication and the Banach space norm are required to be related by the following inequality:
		(i.e., the norm of the product is less than or equal to the product of the norms.) This ensures that the multiplication operation is continuous.
		The set of real (or complex) numbers is a Banach algebra with norm given by the Absolute value.
	www.ufaqs.com /wiki/en/ba/Banach%20algebra.htm (170 words)

	Matrix Norm algorithm: Source
		An approximate matrix condition number is needed for a block wise LU
		Matrix A can represent both A or its effective inverse via
		(approximated) is the spectral norm, which is the largest magnitude
	www.sci4um.com /post-259983.html (642 words)

	Matrix norm
		A sub-multiplicative vector norm refers to a vector norm on square matrices compatible with matrix multiplication in the sense that
		In the remaining article, we will follow the tradition in matrix theory.
		Moreover, when m=n, then for any vector norm
	www.teachersparadise.com /ency/en/wikipedia/m/ma/matrix_norm.html (328 words)

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