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Topic: Trace of a matrix

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Frobenius norm

Unitary matrix

Estimation of covariance matrices

Eigenvalue

Multivariate normal distribution

Maximum likelihood

Normal distribution

	PlanetMath: trace of a matrix (Site not responding. Last check: 2007-10-22)
		The trace of the matrix is the sum of the main diagonal:
		For this reason it is possible to define the trace of a linear transformation, as the choice of basis does not affect the trace.
		This is version 16 of trace of a matrix, born on 2001-11-16, modified 2006-07-19.
	planetmath.org /encyclopedia/TraceOfAMatrix.html (539 words)

	Trace (linear algebra) - Wikipedia, the free encyclopedia
		The use of the term trace arises from the German term Spur (cognate with the English spoor), which, as a function in mathematics, is often abbreviated to "Sp".
		A matrix whose trace is zero is said to be traceless or tracefree.
		The concept of trace of a matrix is generalised to the trace class of compact operators on Hilbert spaces.
	en.wikipedia.org /wiki/Trace_(matrix) (798 words)

	CMSC 455 Lecture 13, Eigenvalues of a Complex Matrix
		Given a matrix A and a non singular matrix P and P inverse p^-1 B = P A P^-1 the matrix B has the same eigenvalues as matrix A. B is a similarity transform of A. The diagonal elements of a diagonal matrix are the eigenvalues of the matrix.
		The trace of a matrix is the sum of the diagonal elements.
		The trace of a matrix is equal to the sum of the eigenvalues.
	www.cs.umbc.edu /~squire/cs455_l13.html (1377 words)

	Matrices
		A matrix A is a rectangular array of numbers, coefficients or variables.
		Rank: the rank of a matrix A, often denoted r(A), is the number of linearly independent rows or columns of that matrix.
		Trace: the trace of a matrix A (denoted trA) is the sum of the elements on the principal diagonal, i.e.
	cepa.newschool.edu /het/essays/math/matrix.htm (945 words)

	Trace and Norm (Site not responding. Last check: 2007-10-22)
		The trace of a square matrix is the sum of its diagonal elements.
		Therefore the trace of ab is the same as the trace* of b*a.
		The trace of t is the sum of the diagonal elements, which happens to be the sum of the eigen values.
	www.mathreference.com /la-sim,trace.html (419 words)

	Matrix Computations (Site not responding. Last check: 2007-10-22)
		The trace of a matrix is the sum of its diagonal components.
		The determinant of a matrix is sometimes tricky to compute.
		For a 2x2 matrix with first row (a, b) and second row (c, d), the determinant is the quantity ad-bc.
	www.geom.uiuc.edu /~fjw/Labs/General/matrix.html (93 words)

	Linear Algebra (Site not responding. Last check: 2007-10-22)
		This command constructs a diagonal matrix, that is a square matrix whose off-diagonal entries are all zero.
		The minor is the determinant of the matrix obtained from M by deleting the i-th row and the j-th column.
		The (i, j)-th element of the Jacobian matrix is defined as the derivative of i-th function with respect to the j-th variable.
	homepage.mac.com /yacas/manual/refchapter9.html (2078 words)

	MAT 200 Lecture Notes -- Lemmas About Matrices
		The diagonal line from the upper left hand corner of a square matrix to the lower right hand corner is called the main diagonal.
		The sum of the entries on the main diagonal of a square matrix A is called the trace of A and is denoted tr(A).
		But the trace of an identity matrix, being the sum of the entries on the main diagonal, all of which are equal to 1, is just the number of rows or columns.
	www.math.princeton.edu /~stalker/200f99/notes_4.html (584 words)

	[No title]
		If aij is the ith row and the jth column element of a nxn matrix [A], then the trace of a nxn matrix is defined as EMBED Equation.3 .
		For example, the trace of EMBED Equation.3 is EMBED Equation.3 EMBED Equation.3 = 17 Specifications: In a single worksheet, write the following program Use restart in the beginning of the worksheet.
		Write a procedure to find the trace of a given square matrix trace_matrix:=proc(n,A) The input parameters are n = number of rows or columns of the square matrix A = square matrix of order nxn You need to use a loop to find the trace of a given square matrix in the procedure.
	www.eng.usf.edu /~kaw/class/EML3035/programs/maple_trace_matrix.doc (346 words)

	Java Script Linear Algebra
		The trace of a matrix is simply the summation of its main diagonal.
		The adjoint of A is the matrix whose i, and jth element is the cofactor A
		The inverse of A is the matrix which when multiplied to A returns the identity matrix.
	www.mkaz.com /math/js_lalg1.html (171 words)

	Matrix Trace (Site not responding. Last check: 2007-10-22)
		If matrix object is a real matrix then the value returned is a Double.
		If matrix object is a complex matrix then the value returned is a Complex.
		Error 1305 will be returned, if matrix is not square.
	www.bluebit.gr /matrix/version_31/Matrix-Trace.htm (38 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).
		The rank of a (mn) matrix* is equal to the rank of the largest sub matrix with a determinant different from zero where the determinant of a matrix is defined by
		The determinant of an orthogonal matrix is equal to 1 or -1.
	www.xycoon.com /matrix_algebra.htm (1855 words)

	Class Matrix
		If this matrix happens to be a 3 X 3 matrix, this method will compute the SVD of it, using Jacobi method This is based on code that was generously provided by cvl.
		The matrix Note that we assume the matrix to be rectangular.
		Multiply the "this" matrix by the matrix M, as in retValue = this * M This helper method automatically allocates the new Matrix for you.
	www.cs.bgu.ac.il /~klara/AhazGal/API/Matrix.html (2070 words)

	WorkingWithMatrices
		You can use TEMATH's Matrix Calculator to do matrix arithmetic, solve systems of linear equations, perform elementary row or column operations, find the inverse of a matrix, find the eigenvalues and eigenvectors of a matrix, calculate the norm, determinant, and trace of a matrix, and much more.
		To enter the 5 X 5 matrix M, where the element in the ith row and jth column is given by mij = i - j r (r is a random number between 0 and 1),
		The inverse matrix is written into the matrix area of the Matrix Calculator window.
	www2.umassd.edu:16080 /temath/TEMATH2/Examples/WorkingWithMatrices.html (1237 words)

	Matrix Trace -- from Wolfram MathWorld
		The matrix trace is implemented in Mathematica as
		The trace of a product of three or more square matrices, on the other hand, is invariant only under cyclic permutations of the order of multiplication of the matrices, by a similar argument.
		The value of the trace can be found using the fact that the matrix can always be transformed to a coordinate system where the z-axis lies along the axis of rotation.
	mathworld.wolfram.com /MatrixTrace.html (169 words)

	Assumed knowledge of matrices and vector spaces
		The transpose of an orthogonal matrix is also orthogonal.
		is a diagonal matrix whose elements are the eigenvalues of
		No idempotent matrix can have negative elements on its diagonal.
	mcs.une.edu.au /~stat354/notes/node13.html (244 words)

	Trace (matrix) - Education - Information - Educational Resources - Encyclopedia - Music (via CobWeb/3.1 ... (Site not responding. Last check: 2007-10-22)
		represents the (i,j)'th element of A. The use of the term trace arises from the German term Spur (cognate with the English spoor).
		A matrix whose trace is zero is said to be traceless.
		The concept of trace of a matrix is generalised to the trace class of bounded linear operators on Hilbert spaces.
	education.music.us.cob-web.org:8888 /T/Trace-(matrix).htm (854 words)

	LIMSource: 1998 LIMS Conference: Presentation Abstract: Trace Matrix Methodology for the Validation of Laboratory ... (Site not responding. Last check: 2007-10-22)
		The Trace Matrix is an electronic or manual charting of links and correlation between systems requirements, system design elements, system software modules or components, and various system tests.
		This paper demonstrates the use of the trace Matrix, applying to the validation of a UniLab4 LIMS operating in the quality control laboratory of a Swiss biotechnology production facility.
		The methods for construction of the Trace Matrix, applications of its use, and function during a regulatory audit all are considered, illustrated, and analyzed.
	www.limsource.com.cob-web.org:8888 /comunity/LIMS12/Abstracts/LIMS98_AB_weinberg.html (177 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Subject: Re: Geometric interpretation of the trace of a matrix?
		For example, > > in the case of the determinant, it is the (signed) volume of the > > parallelepiped formed by all the rows (or columns) of a matrix.
		P_n where P_j is the -geometric mean- of the principal jxj minors of a positive definite and symmetric but not neccessarily diagonal matrix K; in particular P_1 >= P_n is the Hadamard inequality product of diagonal entries >= det K 5.
	www.math.niu.edu /~rusin/known-math/99/matrix_ineq (356 words)

	Math 721
		Additionally the trace of a matrix is the sum of its diagonal elements.
		Prove the following (you may assume that the matrix has entries from a field).
		is similar to a diagonal matrix if and only if there is a basis of
	www.ndsu.nodak.edu /ndsu/coykenda/M721.4.S2001.htm (60 words)

	Table of Contents
		He also looks into special matrices—including complex numbers, quaternion matrices, and matrices with complex entries—transpose matrices; the trace of a matrix; the cross product of matrices; eigenvalues and eigenvectors; and infinite series of matrices.
		Using an Equation Satisfied by a Matrix 3.
		Using the Least Equation Satisfied by a Matrix to Solve the Problem of Reciprocals 5.
	www.doverpublications.com /cgi-bin/toc.pl/0486420000 (238 words)

	Linear Algebra (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-10-22)
		Orthogonal Basis for Null Space of a Matrix
		Orthogonal Basis for Range Space of a Matrix
		Generalized Eigenvalues and Eigenvectors of a General Matrix
	www.omatrix.com.cob-web.org:8888 /manual/linear.htm (40 words)

	Matrix.NET (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-10-22)
		Matrix.NET gives you the classes you need to make it even easier to program matrices and vectors, simply because the vast majority of texts that discuss matrices and vectors use base 1.
		The Matrix and Vector classes comply with.NET 2.0, and play well together.
		Utility functions simplify code production, and the Matrix and Vector classes use a few functions that are missing from.NET.
	www.engineeringobjects.com.cob-web.org:8888 /DotNet/Matrix/matrixdotnet.htm (792 words)

	Singular Manual: matrix related functions
		standard basis and transformation matrix computation (see liftstd)
		set of minors of a matrix (see minor)
		See also the library matrix_lib, which contains more matrix-related functions.
	www.math.lsu.edu /singular/sing_117.htm (36 words)

	Trace The Matrix Download (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-10-22)
		Home > Games > Arcade > Trace The Matrix
		Trace The Matrix - Crazy arcade game with dozens of enemies.
		Neon Wars - This game is a fully mouse controlled abstract shooter style game featuring colorful graphics, special weapons, fully automated fire, and multiple difficulty levels.
	www.shareup.com.cob-web.org:8888 /Tweaki/Trace_The_Matrix-download-7453.html (405 words)

	47.5 Trace of a matrix or the product of two matrices (TRACE) (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-10-22)
		47.5 Trace of a matrix or the product of two matrices (TRACE) (via CobWeb/3.1 planet03.csc.ncsu.edu)
		47.5 Trace of a matrix or the product of two matrices (
		The result of the trace operation is stored in the MOLPRO variable variable, which can be used in subsequent operations.
	www.molpro.net.cob-web.org:8888 /info/current/doc/manual/node576.html (55 words)

	O-Matrix Linear Algebra
		trace - Computing The Trace Of A Matrix
		logdet - Log Of The Determinant Of A Matrix
		eigsym - Eigenvalues And Eigenvectors Of A Symmetric Matrix
	www.aspiresoftwareintl.com /html/o-matrix_linear_algebra.html (164 words)

	36.5 Trace of a matrix or the product of two matrices (TRACE) (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-10-22)
		36.5 Trace of a matrix or the product of two matrices (TRACE) (via CobWeb/3.1 planet03.csc.ncsu.edu)
		36.5 Trace of a matrix or the product of two matrices (
		If factor is not given, one is assumed.
	its.unc.edu.cob-web.org:8888 /asg/applications/molpro/manual/node528.html (55 words)

	taking trace of matrix - dBforums (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-10-22)
		If you would prefer not to see any double-underlined words and corresponding advertisements, please click here.
		Just for fun, I wrote a one-liner to do the trace of a matrix:
		Not necessarily the most transparent solution, I admit.
	dbforums.com.cob-web.org:8888 /t849769.html (225 words)

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