
	Where results make sense

Topic: Matrix exponential

Related Topics

Jordan normal form

Orthogonal matrix

RLC circuit

Normal distribution

New tribalists

Annabel Vane Tempest Stewart

In the News (Wed 23 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	PlanetMath: diagonal matrix
		The identity matrix and zero matrix are diagonal matrices.
		The matrix exponential of a diagonal matrix is
		This is version 9 of diagonal matrix, born on 2003-06-28, modified 2006-05-25.
	planetmath.org /encyclopedia/DiagonalMatrix.html (199 words)

	Matrix (mathematics) - Wikipedia, the free encyclopedia
		The entry of a matrix A that lies in the i -th row and the j-th column is called the i,j entry or (i,j)-th entry of A.
		The rank of a matrix A is the dimension of the image of the linear map represented by A; this is the same as the dimension of the space generated by the rows of A, and also the same as the dimension of the space generated by the columns of A.
		The trace of a square matrix is the sum of its diagonal entries, which equals the sum of its n eigenvalues.
	en.wikipedia.org /wiki/Matrix_(mathematics) (1577 words)

	[No title]
		Matrix ill-conditioning is a general term used to describe a rectangular matrix of values which is unsuitable for use in a particular analysis.
		In this type of Matrix Plot, a matrix of X-Y (i.e., nonsequential) line plots (similar to a scatterplot matrix) is produced in which individual points are connected by a line in the order of their appearance in the data file.
		The column (or row) rank of a rectangular matrix of values (e.g., a sums of squares and cross-products matrix) is equal to the number of linearly independent columns (or rows) of elements in the matrix.
	www.statsoft.com /textbook/glosm.html (5420 words)

	Matrix Exponentiation
		It is not generally known that matrix exponentiation may be used to solve sets of kinetic differential equations where all rates are first order.
		Recalling that exponentials are normalized to unity the initial concentrations of A and B are the 1 and 0.
		Matrix Exponentiation is thus a more general kind of exponentiation: the beauty of the Exponential Matrix method is that it may be easily extended to much more complicated cases with many first order processes including reversible steps.
	www.olisweb.com /software/matrixexp.php (507 words)

	MATRIX
		Exponential operator is applied to each element of matrix.
		A matrix with ndim rows and columns is created with a diagonal of ones on the ndiag lower diagonal.
		A new matrix with n rows is created by random sampling with replacement from the old matrix.
	shazam.econ.ubc.ca /~diana/ref/matrix.htm (167 words)

	Matrix Reference Manual: Special Matrices
		A 3#3 orthogonal matrix is either a rotation matrix or else a rotation matrix plus a reflection in the plane of the rotation according to whether it is proper or improper.
		A Rotation matrix is orthogonal with a determinant of +1.
		A signature matrix is a diagonal matrix whose diagonal entries are all +1 or -1.
	www.ee.uwa.edu.au /~roberto/teach/matrix/special.html (4269 words)

	Matrix Exponential
		The matrix exponential plays an important role in solving system of linear differential equations.
		This notation is natural due to the properties of this matrix.
		Assume that all its entries on the diagonal are equal to 0.
	www.sosmath.com /matrix/expo/expo.html (317 words)

	Matrix Reference Manual: Special Matrices
		A 3#3 orthogonal matrix is either a rotation matrix or else a rotation matrix plus a reflection in the plane of the rotation according to whether it is proper or improper.
		Every 3#3 orthogonal matrix is either a rotation matrix or else a rotation matrix plus a reflection in the plane of the rotation according to whether its determinant is +1 or -1.
		A signature matrix is a diagonal matrix whose diagonal entries are all +1 or -1.
	www.ee.ic.ac.uk /hp/staff/dmb/matrix/special.html (4464 words)

	CKM matrix exponential parametrization and Euler angles (Site not responding. Last check: 2007-10-10)
		In a number of previous papers we have shown that the exponential parametrization of the CKM matrix offers a useful tool to deal with the weak quark mixing [1-3] and provides an effective analytical method to derive mass matrices and weak interaction eigenstates [4].
		One of the characterizing elements of the exponential parametrization of the CKM is that it naturally incorporates the Wolfenstein hierarchy [7].
		Equation (19a) provides a Wolfenstein-like form of the CKM matrix in the limit in which the CP violation, are assumed to be not of CKM origin.
	www.sif.it /cimento/toca/110.05/03/03.html (1130 words)

	Exponential function Summary
		Scientists from various fields use exponential functions as models for growth and decay phenomena in which a quantity is assumed to grow or decay at a rate which is proportional to the amount of the quantity at any given time.
		Exponential functions and modifications of exponential functions are currently being used to study such phenomena as the growth of the internet, the spread of AIDS, the projected growth or decay of the national debt, and much more.
		The definition of the exponential function given above can be used verbatim for every Banach algebra, and in particular for square matrices (in which case the function is called the matrix exponential).
	www.bookrags.com /Exponential_function (1700 words)

	Matrix Manual: Special Matrices
		matrix, A, is an nn Toeplitz matrix* in which a(i,j) is a function of {(i-j) modulo n}.
		A is symmetric iff it is congruent to a diagonal matrix.
		Any square matrix may be uniquely decomposed as the sum of a symmetric matrix and a skew-symmetric matrix.
	www.psi.toronto.edu /matrix/special.html (2192 words)

	A note on parameter differentiation of matrix exponentials, with applications to continuous-time modelling, Henghsiu ...
		The new formula expresses the derivatives of a matrix exponential in terms of minors, polynomials, the exponential of the matrix as well as matrix inversion, and hence is algebraically more manageable.
		For the companion matrix of a continuous-time autoregress\-ive moving average process, the derivatives of the exponential of the companion matrix can be computed recursively.
		The second example concerns the exponential of the tri\-diagonal transition intensity matrix of a finite-state-space continuous-time Markov chain whose instantaneous transitions must be between adjacent states.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.bj/1066418883 (300 words)

	System Dynamics Mathematical Background Review of Matrix Algebra and Matrix Calculus
		matrix is the determinant of the matrix formed by deleting the i
		where the adjoint matrix is formed by replacing each element of a matrix by its cofactor and then taking the transpose.
		A singular matrix is one whose determinant is zero.
	gershwin.ens.fr /vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/sdyn/s2/s2mamc/s2mamc.html (555 words)

	MIMS EPrints - 2006.394: The Scaling and Squaring Method for the Matrix Exponential Revisited
		The scaling and squaring method is the most widely used method for computing the matrix exponential, not least because it is the method implemented in MATLAB's {\tt expm} function.
		The method scales the matrix by a power of 2 to reduce the norm to order 1, computes a Padé approximant to the matrix exponential, and then repeatedly squares to undo the effect of the scaling.
		Our implementation of the scaling and squaring method always requires at least two fewer matrix multiplications than {\tt expm} when the matrix norm exceeds 1, which can amount to a 37% saving in the number of multiplications, and it is typically more accurate, owing to the fewer required squarings.
	eprints.ma.man.ac.uk /634 (344 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		The standard Taylor's series expansion uses powers of the K matrix whereas an alternative block-matrix representation of K and its powers exploits the symmetry that is present in the matrix EXP(K).
		The matrix approximation to EXP(K) employed in SCF minimizations should be accurately orthogonal as well as appropriately close to the exponential value.
		In contrast to a truncated Taylor series, the Pade' approximations to the matrix exponential are orthogonal by construction.
	www.emsl.pnl.gov /proj/tms/hpcc_actinides/research-98/argonne/Pade.html (479 words)

	SYLVESTER'S MATRIX THEOREM
		The identity matrix may be expanded in terms of the eigenvectors of the matrix A.
		Postmultiply (33) by the row matrix and premultiply by the column matrix.
		The exponential matrix is a solution to the differential equation (37) without regard to boundaries.
	sepwww.stanford.edu /ftp/prof/fgdp/c5/paper_html/node3.html (838 words)

	Matrix Exponential
		The matrix exponential in the frequency domain is given as well through treatment by the Laplace transform.
		However, in the case of the matrix exponential, this is not true.
		The derivative operates on the matrix exponential the same as it does on the scalar exponential.
	cnx.org /content/m2112/2.10 (437 words)

	SYLVESTER'S MATRIX THEOREM
		The identity matrix may be expanded in terms of the eigenvectors of the matrix A.
		Postmultiply (33) by the row matrix and premultiply by the column matrix.
		The exponential matrix is a solution to the differential equation (37) without regard to boundaries.
	sep.stanford.edu /sep/prof/fgdp/c5/paper_html/node3.html (838 words)

	LPPD, University of Illinois at Chicago
		Addition and subtraction require both matrices to have the same dimension, or one of them to be a scalar (a scalar matrix is a 1-by-1 matrix).
		Inverses and Determinants: The inverse of a matrix is computed by the function inv and the determinant by the function det.
		Matrix powers: If A is a square matrix and ‘p’ is a positive integer, then A^p multiplies A by itself ‘p’ times.
	vienna.che.uic.edu /teaching/che431/Introduction_To_Matlab.htm (1240 words)

	Dom::Matrix
		Many system functions are overloaded for matrices, such as map, subs, has, zip, E.g., use conjugate to compute the complex conjugate of a matrix, norm to compute matrix norms, or exp to compute the exponential of a matrix.
		The components of a matrix are no longer evaluated after the creation of the matrix, i.e., if they contain free identifiers they will not be replaced by their values.
		If x is a matrix of the same type as A or can be converted into a matrix of the same type as A and the indices i or j are ranges corresponding to a submatrix of A, then x replaces the corresponding submatrix in A.
	www.sciface.com /support/doc/40/de/Dom/Matrix.html (6410 words)

	Case of #tex2html_wrap_inline33966#: Alternative and/or existing variants pertaining to Type 2 classification of time ...
		Alternatively, instead of directly computing the exponential matrix term, Fung [28] suggested an alternative way to obtain the exponential matrix leading to implicit unconditionally stable representations.
		Rational/Padé approximation and sub-stepping belong to a family of matrix identical approaches for approximating the exponential matrix.
		It is convenient to approximate the exponential matrix in the rational form and we describe an effective time discretized operator.
	www-users.cs.umn.edu /~xiangmin/arc/node46.html (870 words)

	Graphs of Functions and Algebra - Interactive Tutorials
		Exponential functions are explored, interactively, using an applet.
		A graph is generated and you are supposed to find a possible formula for the exponential function corresponding to the given graph.
		Exponential and power functions are compared interactively, using an applet.
	www.analyzemath.com /precalculus.html (1288 words)

	PlanetMath: matrix exponential
		Then the matrix exponential satisfies the following properties
		Cross-references: rotational matrix, inverse, determinant, trace, invertible, identity matrix, zero matrix, properties, square, formula, diagonal matrix, diagonalizable, natural number, nilpotent, matrix, converges, bounded, matrix norms, order, square matrix, real, exponential
		This is version 8 of matrix exponential, born on 2003-04-06, modified 2006-08-10.
	planetmath.org /encyclopedia/MatrixExponential.html (124 words)

	Welcome to Wasin So
		The object of study is the matrix exponential.
		The only new result is a necessary condition on the singular values of a matrix and those of its exponential.
		Finally, as an application of matrix exponential formulas, three different types of spectral indices are proved to be equivalent in Chapter 5.
	www.sjsu.edu /faculty/wso/phd_thesis.htm (554 words)

	BioMed Central \| Full text \| Evolutionary models for insertions and deletions in a probabilistic modeling framework
		For instance, the HKY model for nucleotide substitutions [48] depends on six parameters: the four stationary nucleotide frequencies, a rate of transitions, and a rate of transversions, which have to be provided externally.
		It is relevant to compare instantaneous rate matrix approaches to the approach used in the PAM amino-acid substitution matrices [53].
		This rate matrix assumes that the rate of change in the occurrence of state M' is similar to that of state D' and that of state I, and that this change reverts equally into the other two states.
	www.biomedcentral.com /1471-2105/6/63 (9224 words)

	Honors Projects
		The solution can also be expressed as an exponential matrix function when the matrix has distinct, real eigenvalues.
		John Noonan showed in his paper how to find that exponential matrix when the eigenvalues are repeated, real values.
		While he found an expression for an exponential matrix with repeated real eigenvalues, Karen Pease found an expression for an exponential matrix with multiple complex roots.
	campus.houghton.edu /orgs/mathematics/honors.html (659 words)

	expm (MATLAB Function Reference) (Site not responding. Last check: 2007-10-10)
		A second method of calculating the matrix exponential uses a Taylor series approximation.
		, is to diagonalize the matrix, apply the function to the individual eigenvalues, and then transform back.
		Notice that the diagonal elements of the two results are equal; this would be true for any triangular matrix.
	www.eco.utexas.edu /helpdocs/matlab/ref/expm.html (196 words)

	PhD Thesis Page
		The object of study is the matrix exponential.
		The only new result is a necessary condition on the singular values of a matrix and those of its exponential.
		Finally, as an application of matrix exponential formulas, three different types of spectral indices are proved to be equivalent in Chapter 5.
	www.math.sjsu.edu /~so/pthesis.html (514 words)

Try your search on: Qwika (all wikis)