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Topic: Diagonalizable

	Diagonalizable matrix - Wikipedia, the free encyclopedia
		Diagonalizable matrices and maps are of interest because diagonal matrices are especially easy to handle: their eigenvalues and eigenvectors are known and one can raise a diagonal matrix to a power by simply raising the diagonal entries to that same power.
		A linear map T : V → V is diagonalizable if and only if the sum of the dimensions of its eigenspaces is equal to dim(V), which is the case if and only if there exists a basis of V consisting of eigenvectors of T.
		One can also say that the diagonalizable matrices form a dense subset with respect to the Zariski topology: the complement lies inside the set where the discriminant of the characteristic polynomial vanishes, which is a hypersurface.
	en.wikipedia.org /wiki/Diagonalizable_matrix (783 words)

	Diagonalizable matrix -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-07)
		In (The part of algebra that deals with the theory of linear equations and linear transformation) linear algebra, a square matrix A is called diagonalizable if it is (additional info and facts about similar) similar to a (A square matrix with all off-diagonal elements equal to zero) diagonal matrix, i.e.
		Diagonalizable matrices and maps are of interest because diagonal matrices are especially easy to handle: their (additional info and facts about eigenvalue) eigenvalues and (additional info and facts about eigenvector) eigenvectors are known and one can raise a diagonal matrix to a power by simply raising the diagonal entries to that same power.
		One can also say that the diagonalizable matrices form a dense subset with respect to the (additional info and facts about Zariski topology) Zariski topology: the complement lies inside the set where the (additional info and facts about discriminant) discriminant of the characteristic polynomial vanishes, which is a (additional info and facts about hypersurface) hypersurface.
	www.absoluteastronomy.com /encyclopedia/d/di/diagonalizable_matrix.htm (790 words)

	Station Information - Diagonalizable
		If V is a finite-dimensionalal vector space, then a linear map T : V → V is called diagonalizable if there exists a basis of V with respect to which T is represented by a diagonal matrix.
		An n-by-n matrix A over the field F is diagonalizable if and only if the sum of the dimensionss of its eigenspaces is equal to n, which is the case if and only if there exists a basis of F
		A linear map T : V → V is diagonalizable if and only if the sum of the dimensionss of its eigenspaces is equal to dim(V), which is the case if and only if there exists a basis of V consisting of eigenvectors of T.
	www.stationinformation.com /encyclopedia/d/di/diagonalizable.html (600 words)

	Encyclopedia: Diagonalizable matrix (Site not responding. Last check: 2007-10-07)
		In mathematics, a subset B of a vector space V is said to be a basis of V if it satisfies one of the four equivalent conditions: B is both a set of linearly independent vectors and a generating set of V. B is a minimal generating set of V...
		In mathematics, a number is called an eigenvalue of a matrix if there exists a nonzero vector such that the matrix times the vector is equal to the same vector multiplied by the eigenvalue.
		In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers.
	www.nationmaster.com /encyclopedia/Diagonalizable-matrix (1516 words)

	Diagonalizable matrix (Site not responding. Last check: 2007-10-07)
		If V is a finite- dimensional vector space, then a linear map T :V → V is called diagonalizable if there exists a basis of V with respect to which T isrepresented by a diagonal matrix.
		Diagonalizable matrices and maps are of interest because diagonal matrices are especially easy to handle: their eigenvalues and eigenvectors areknown and one can raise a diagonal matrix to a power by simply raising the diagonal entries to that same power.
		An n-by-n matrix A over the field F is diagonalizable if and only if the sum of the dimensions of its eigenspaces is equal ton, which is the case if and only if there exists a basis of F
	www.therfcc.org /diagonalizable-matrix-272002.html (570 words)

	Diagonalizable (Site not responding. Last check: 2007-10-07)
		A matrix m is diagonalizable if it is similar to a diagonal matrix.
		Therefore every diagonalizable matrix (which is similar to a diagonal matrix) has n independent eigen vectors.
		Therefore a matrix is diagonalizable iff it has n independent eigen vectors.
	www.mathreference.com /la-sim,diag.html (240 words)

	PlanetMath: example of non-diagonalizable matrices (Site not responding. Last check: 2007-10-07)
		Some matrices with real entries which are not diagonalizable over
		But there exist real matrices which aren't diagonalizable even if complex eigenvectors and eigenvalues are allowed.
		Cross-references: columns, diagonalization, kernel, vectors, identity, complex, diagonalize, eigenvectors, linearly independent, eigenvalues, complex numbers, diagonalizable, real, matrices
	planetmath.org /encyclopedia/ExampleOfNonDiagonalizableMatrices2.html (107 words)

	Diagonalizable matrix - Encyclopedia, History, Geography and Biography
		Diagonalizable matrix - Encyclopedia, History, Geography and Biography
		This matrix is not diagonalizable: there is no matrix U such that $U^{-1}CU$ is a diagonal matrix.
		Diagonalizable matrix, Examples, How to diagonalize a matrix, Matrices that are not diagonalizable, An application, See also, External links and References.
	www.arikah.net /encyclopedia/Matrix_diagonalization (1043 words)

	Rank complement of diagonalizable matrices using polynomial functions
		This report defines the rank complement of a diagonalizable matrix (i.e.
		These results are then generalized to the case of diagonalizable matrices.
		Finally, a Matlab function is described that implements a rank complement operation based on the results derived.
	www.cvl.isy.liu.se /ScOut/TechRep/PaperInfo/kngf2001.html (274 words)

	► » Diagonalizable matrices (Site not responding. Last check: 2007-10-07)
		Let D be the subset of M of all diagonalizable matrices.
		My question is: is D a dense subset of M with respect to the Zariski
		eigenvalues is diagonalizable over an algebraically closed field.
	www.science-chat.org /Diagonalizable-matrices-5838047.html (610 words)

	4.2. Diagonalizable matrices
		A is diagonalizable if it is similar to a diagonal matrix B.
		An n x n matrix A is diagonalizable if and only if it has n linearly independent eigenvectors.
		If the eigenvalues of A are all distinct, their corresponding eigenvectors are linearly independent and therefore A is diagonalizable.
	www.ee.oulu.fi /~mpa/matreng/ematr4_2.htm (215 words)

	Eigenvalue and Eigenvector 3
		A matrix is diagonalizable if it has any of the following equivalent properties
		The first property can also be used to define the diagonalizability for linear transformations
		does not have a basis of eigenvectors and is not diagonalizable.
	algebra.math.ust.hk /eigen/01_definition/lecture3.shtml (176 words)

	Re: Diagonalizable matrices
		Consider the space M of all square matrices with n lines, n rows and entries in k.
		My question is: is D a dense subset of M with respect to the Zariski topology?
		The reason is that any matrix with distinct eigenvalues is diagonalizable over an algebraically closed field.
	www.usenet.com /newsgroups/sci.math/msg21987.html (246 words)

	Isospectral - Wikipedia, the free encyclopedia
		In the case of operators on infinite-dimensional spaces, the spectrum need not consist solely of isolated eigenvalues; the rest of this article will assume for clarity that we are talking about operators on finite-dimensional vector spaces.
		In that case, for complex square matrices, the relation of being isospectral for two diagonalizable matrices is just similarity.
		This doesn't however reduce completely the interest of the concept, since we can have an isospectral family of matrices of shape A(t) = M(t)
	en.wikipedia.org /wiki/Isospectral (234 words)

	System of Phase Oscillators with Diagonalizable Interaction
		System of Phase Oscillators with Diagonalizable Interaction: SIAM Journal on Applied Mathematics Vol.
		We consider a system of N phase oscillators having randomly distributed natural frequencies and diagonalizable interactions among the oscillators.
		We show that, in the limit of $N \to \infty$, all solutions of such a system are incoherent with probability one for any strength of coupling, which implies that there is no sharp transition from incoherence to coherence as the coupling strength is increased, in striking contrast to Kuramoto's (special) oscillator system.
	epubs.siam.org /sam-bin/dbq/article/41113 (145 words)

	diagonalizable matrix - OneLook Dictionary Search (Site not responding. Last check: 2007-10-07)
		We found 2 dictionaries with English definitions that include the word diagonalizable matrix:
		Tip: Click on the first link on a line below to go directly to a page where "diagonalizable matrix" is defined.
		Diagonalizable Matrix : Eric Weisstein's World of Mathematics [home, info]
	public.onelook.com /?w=diagonalizable+matrix (81 words)

	Diagonalizable Matrices
		More generally, the following theorem helps us detect diagonalizable matrices and, also, to diagonalize them.
		is diagonalizable if and only if the following conditions hold:
		We have seen that diagonalizing a matrix helps us in determining the transformation properties of a given matrix.
	www.ualberta.ca /dept/math/gauss/fcm/LinAlg/InRn/EigenThry/Dgnlzbl.htm (64 words)

	A Parallelizable Eigensolver for Real Diagonalizable Matrices with Real Eigenvalues - Lederman, Tsao, Turnbull ... (Site not responding. Last check: 2007-10-07)
		In this paper, preliminary research results on a new algorithm for finding all the eigenvalues and eigenvectors of a real diagonalizable matrix with real eigenvalues are presented.
		The basic mathematical theory behind this approach is reviewed and is followed by a discussion of the numerical considerations of the actual implementation.
		A parallelizable eigensolver for real diagonalizable matrices with real eigenvalues.
	citeseer.lcs.mit.edu /huss-lederman97parallelizable.html (739 words)

	Diagonalizable (Site not responding. Last check: 2007-10-07)
		The word "diagonalizable" uses 14 letters: A A A B D E G I I L L N O Z.
		Words within diagonalizable not shown as it has more than seven letters.
		List all words starting with diagonalizable, words containing diagonalizable or words ending with diagonalizable
	www.morewords.com /word/diagonalizable (140 words)

	IngentaConnect Diagonalizable Extended Backward Differentiation Formulas (Site not responding. Last check: 2007-10-07)
		We generalize the extended backward differentiation formulas (EBDFs) introduced by Cash and by Psihoyios and Cash so that the system matrix in the modified Newton process can be block-diagonalized, enabling an efficient parallel implementation.
		The purpose of this paper is to justify the use of diagonalizable EBDFs on parallel computers and to offer a starting point for the development of a variable stepsize-variable order method.
		We construct methods which are L-stable up to order p = 6 and which have the same computational complexity per processor as the conventional BDF methods.
	www.ingentaconnect.com /content/klu/bitn/2000/00000040/00000003/00331275 (205 words)

	Higher algebraic K-theory for actions of diagonalizable groups, by Gabriele Vezzosi and Angelo Vistoli (Site not responding. Last check: 2007-10-07)
		Higher algebraic K-theory for actions of diagonalizable groups, by Gabriele Vezzosi and Angelo Vistoli
		We study the K-theory of actions of diagonalizable group schemes on regular algebraic spaces: our main result shows how to reconstruct the K-theory ring of such an action from the K-theory rings of the loci where the stabilizers have constant dimension.
		We apply this to the calculation of the equivariant K-theory of toric varieties, give conditions under which the Merkurjev spectral sequence degenerates, and prove a very refined localization theorem.
	www.math.uiuc.edu /K-theory/0506 (98 words)

	MathLinks Math Forum :: View topic - interior of diagonalizable matrices (Site not responding. Last check: 2007-10-07)
		Posted: Tue 02 Nov 2004, 15:13 Post subject: interior of diagonalizable matrices
		In the first case (when we deal with complex matrices), I believe the interior consists of those diagonalizable matrices which have distinct eigenvalues.
		We may as well assume that we're working with diagonal matrices, and if there are two equal eigenvalues, then the first two diagonal entries are equal.
	www.mathlinks.ro /Forum/post-127962.html (419 words)

	Provability Logic
		provability algebras, also called diagonalizable algebras or Magari algebras (see Shavrukov (1993, 1997)).
		Shavrukov, V.Y., “A Note on the Diagonalizable Algebras of PA and ZF,” Annals of Pure and Applied Logic, Vol.
		Shavrukov, V.Y., “Undecidability in Diagonalizable Algebras,” Journal of Symbolic Logic, Vol.
	plato.stanford.edu /entries/logic-provability (4840 words)

	IngentaConnect Bures fidelity for diagonalizable quadratic Hamiltonians in multi... (Site not responding. Last check: 2007-10-07)
		IngentaConnect Bures fidelity for diagonalizable quadratic Hamiltonians in multi...
		In this paper we study the Bures fidelity for thermal states of a diagonalizable quadratic Hamiltonian in multi-mode Fock space.
		To the best of our knowledge, no one has yet attempted to give an explicit general formula of fidelity of mixed states in multi-mode systems.
	api.ingentaconnect.com /content/iop/jphysa/2000/00000033/00000027/art00310 (183 words)

	diagonalizable : Definition from the Online Dictionary at Datasegment.com (Site not responding. Last check: 2007-10-07)
		diagonalizable : Definition from the Online Dictionary at Datasegment.com
		2 definitions found diagonalizable - Collaborative International Dictionary of English v.0.48 : diagonalizable \diagonalizable\ adj.
		[PJC] diagonalizable - WordNet (r) 2.0 (August 2003) : diagonalizable adj : capable of being transformed into a diagonal matrix
	onlinedictionary.datasegment.com /word/diagonalizable (53 words)

	AoPS Math Forum :: View topic - interior of diagonalizable matrices
		AoPS Math Forum :: View topic - interior of diagonalizable matrices
		Posted: Tue Nov 02, 2004 5:13 am Post subject: interior of diagonalizable matrices
		Posted: Sat May 07, 2005 5:19 am Post subject:
	www.artofproblemsolving.com /Forum/topic-19084.html (439 words)

	IngentaConnect Gm,np,q-system II and diagonalizable timelike immersions in Rp,m (Site not responding. Last check: 2007-10-07)
		IngentaConnect Gm,np,q-system II and diagonalizable timelike immersions in Rp,m
		In this paper, we study the relation between the G
		Firstly, we construct a dressing action of a simple element on the space of solutions of the G
	api.ingentaconnect.com /content/iop/ip/2004/00000020/00000002/art00001 (147 words)

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