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	PlanetMath: Jordan canonical form theorem
		A Jordan block or Jordan matrix is a matrix of the form
		"Jordan canonical form theorem" is owned by Mathprof.
		This is version 11 of Jordan canonical form theorem, born on 2002-08-26, modified 2006-11-03.
	planetmath.org /encyclopedia/JordanCanonicalForm.html (111 words)

	China encyclopedia : Cultural Information , Maps, China politics and officials, China History. Travel to China
		This word is used by theologians and canon lawyers to refer to the canons of the Roman Catholic, Eastern Orthodox and Anglican Churches adopted by ecumenical councils.
		Canonical can also mean "part of the canon", i.e., one of the books comprising the biblical canon, as opposed to apocryphal books.
		Canonical variables are essential in the Hamiltonian formulation of physics, which is particularly important in quantum mechanics.
	www.chinaiworld.com /wiki-Canonical (801 words)

	Orðasafn: J (Site not responding. Last check: 2007-10-28)
		Jordan arc einfaldur bogi, einfaldur ferill, = simple arc.
		Jordan canonical form kórgerð Jordans, Jordan-kórgerð, Jordan-gerð, = Jordan form, = Jordan normal form, -> canonical form.
		Jordan curve Jordan-ferill, einfaldur lokaður ferill, = simple closed curve.
	www.hi.is /~mmh/ord/safn/safnJ.html (83 words)

	Representing a Class of Similar Matrices
		Every matrix m is similar to a jordan canonical matrix j, and j serves as the "canonical representative" for the class of matrices similar to m.
		The jordan blocks that are nilpotent are the ones with 0 on the main diagonal, i.e.
		The size distribution is the same, at least for the eigen value l, and since l was arbitrary, the canonical forms are the same.
	www.mathreference.com /la-jf,rep.html (1240 words)

	Using the Symbolic Math Toolbox (Symbolic Math Toolbox)
		The Jordan canonical form results from attempts to diagonalize a matrix by a similarity transformation.
		The Jordan form has the eigenvalues on its diagonal, but some of the superdiagonal elements are one, instead of zero.
		The Jordan form is extremely sensitive to perturbations.
	www-rohan.sdsu.edu /doc/matlab/toolbox/symbolic/ch216.html (242 words)

	Jordan Canonical Form
		The block diagonal system having the eigenvalues along the diagonal and ones in some of the superdiagonal elements (which serve to couple repeated eigenvalues) is called Jordan canonical form.
		Each block size corresponds to the multiplicity of the repeated pole.
		Interestingly, neither Matlab nor Octave seem to have a numerical function for computing the Jordan canonical form of a matrix.
	ccrma.stanford.edu /~jos/filters/Jordan_Canonical_Form.html (261 words)

	Kronecker Canonical Form
		In addition to Jordan blocks for finite and infinite eigenvalues, the Kronecker form contains singular blocks corresponding to minimal indices of a singular pencil (see below).
		This fact is utilized in algorithms for computing canonical structure of matrix pencils.
		We end this introductory description by briefly pointing to the relationship between structure information of the KCF and the GUPTRI form (8.28).
	www.cs.utk.edu /~dongarra/etemplates/node309.html (344 words)

	tobepub02 (Site not responding. Last check: 2007-10-28)
		use the Jordan canonical form to show that the statement is as least superficial and sometimes wrong.
		Systems with multiple eigenvalues can be transferred into the Jordan canonical form by a similarity transformation, V, obtained by using system characteristic vectors.
		However, it would help students meeting the Jordan canonical form for the first time to be provided with a method that explains how the characteristic vectors can be determined in an unambiguous way.
	www.ijee.dit.ie /articles/tobepub02.html (181 words)

	Canonical Form (Site not responding. Last check: 2007-10-28)
		A matrix is in jordan canonical form if it is block diagonal, and each block is a simple jordan block.
		Any nilpotent matrix m is similar to a matrix in jordan canonical form.
		(This was proved in the previous section.) The jordan blocks all have zeros on the main diagonal, e.g.
	www.mathreference.com /la-jf,canon.html (116 words)

	Math Forum - Ask Dr. Math
		For example, find the Jordan Canonical Form of: A = [(3 1 2),(0 3 0),(0 0 3)] I approached the problem by finding [lambda I-A].
		Date: 04/29/98 at 11:21:32 From: Doctor Rob Subject: Re: Jordan Canonical Form First you need to find the elementary divisors of A. They will be divisors of the minimal polynomial.
		The matrix S then should be: S = [(0 0 1),(-2 1 3),(1 0 0)] S^(-1) = [(0 0 1),(-3 1 2),(1 0 0)] S^(-1)AS = [(3 0 0),(0 0 -9),(0 1 6)] To convert this into Jordan Form, the first basis element can remain the same, but the last two must change.
	mathforum.org /library/drmath/view/51981.html (455 words)

	The Dimension of Matrices (Matrix Pencils) with Given Jordan (Kronecker) Canonical Forms (Site not responding. Last check: 2007-10-28)
		Abstract: The set of n by n matrices with a given Jordan canonical form defines a subset of matrices in complex n2 dimensional space.
		The new approach is based upon and meant to give insight into the staircase algorithm for the computation of the Jordan Canonical Form as well as the occasional failures of this algorithm.
		We extend both techniques to count the dimension of the more complicated set defined by the Kronecker canonical form of an arbitrary rectangular matrix pencil A-lambda*B.
	techreports.lib.berkeley.edu /accessPages/CSD-92-706.html (122 words)

	jordan (Symbolic Math Toolbox) (Site not responding. Last check: 2007-10-28)
		Thus, its elements must be integers or ratios of small integers.
		Any errors in the input matrix may completely change the Jordan canonical form.
		, the Jordan canonical form, and the similarity transform,
	www.weizmann.ac.il /matlab/toolbox/symbolic/jordan.html (99 words)

	jordan.html (Site not responding. Last check: 2007-10-28)
		This Maple worksheet illustrates the calculation of the Jordan canonical form for the polynomial of Example 5.5, which is further discussed in section 5.1.4 of the textbook.
		The closest form to a diagonal form is the so-called Jordan canonical form:
		Q^(-1).C.Q; Since J is not diagonal, the three last columns of Q are not eigenvectors in the usual sense, they are generalized eigenvectors.
	www.math.uic.edu /~jan/mcs563/jordan1.html (226 words)

	Canonical Form (Site not responding. Last check: 2007-10-28)
		By Juan Vidal-Puga and Gustavo Bargantinños; Abstract: We define the canonical form of a cost spanning tree problem.
		This canonical form is a possibly distorted version...
		All logical functions are expressible in canonical form,...
	www.canonicalform.info (308 words)

	Canonical Forms
		Over fields, a fast algorithm due to Allan Steel is used to construct the various matrix canonical forms: generalized Jordan, rational, and primary rational [
		Over an Euclidean domain, algorithms of Havas and others are used to compute characteristic polynomials and the Hermite and Smith normal forms.
		matrix over Z with random one-digit entries Magma finds its Smith form in 1.3 seconds (the largest elementary divisor is 50 digits) and its characteristic polynomial in 46 seconds.
	magma.maths.usyd.edu.au /magma/Features/node152.html (103 words)

	JORDAN CANONICAL FORM
		What is the ‘nicest’ form we can get an arbitrary matrix into.
		These will then form our matrix M. So, if we can show that the n generalized eigenvectors are linearly independent, and that each one ‘block diagonalizes’ where it should, it is enough to study each l separately.
		For now, we assume their existence (and linear independence), and complete the proof of Jordan Canonical Form.
	www.math.brown.edu /~sjmiller/54/683L/mynotes/weblinalgnotesJordanCanonicalForm.htm (2003 words)

	Jordan Form
		For this purpose we will use their Jordan canonical forms.
		The basic theorem on Jordan canonical form, which we will not state or prove here, says that every square matrix is similar to a direct sum of Jordan blocks over the complex numbers, and this repressentation is unique up to the ordering of the blocks.
		An interesting observation is, that if a matrix has the Jordan form as in (1) then the spectrum of
	www.math.ku.dk /ma/kurser/symbolskdynamik/konjug/node14.html (286 words)

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