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Matrix exponential

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group.

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Overview

Properties

The exponential of sums

Inequalities for exponentials of Hermitian matrices

The exponential map

Computing the matrix exponential

Evaluation by Laurent series

Evaluation by implementation of Sylvester's formula

Illustrations

Applications

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Matrix exponential

Nodes104
Edges103
Triples100
Avg. degree1.98
Density0.019231
Components1

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Matrix exponential

Top relations

related to References · 50
Matrix exponential → Alston, An, Applications, Bibcode, Brian, Cambridge University Press, Charles, Cleve, Compute, Curtright, Decomposition, Dover Books, Exponential, Fairlie, Geometry, Graduate Texts, Hall, Householder, Integrability, ISBN
related to Linear differential equations · 8
Matrix exponential → Ae, At, If, Making, Recall, Rightarrow, See, The
related to Computing the matrix exponential · 7
Matrix exponential → Finding, GNU Octave, In, Matlab, Padé, SciPy, Subsequent
related to Evaluation by Laurent series · 6
Matrix exponential → By, Cayley, Hamilton, If, Qt, To
related to Linear differential equation systems · 5
Matrix exponential → At, Ay, One, See, The
related to The exponential map · 5
Matrix exponential → For, GL, In, The, This
related to Real symmetric matrices · 4
Matrix exponential → Let, S/2, The, Using
related to Elementary properties · 3
Matrix exponential → Let, The, We
related to External links · 3
Matrix exponential → Eric, MathWorld, Weisstein
related to Inequalities for exponentials of Hermitian matrices · 3
Matrix exponential → For Hermitian, Hermitian, If

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Important terminology

displaystyle matrix exponential begin end frac right matrices left exp aligned formula bmatrix -1 solution series sum case form equation

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SubjectPredicateObjectConfidenceSrc
Matrix exponentialis amatrix function on square matrices analogous to the ordinary exponential function0.90text
Matrix exponentialrelated to Computing the matrix exponentialFinding0.60section
Matrix exponentialrelated to Computing the matrix exponentialMatlab0.60section
Matrix exponentialrelated to Computing the matrix exponentialGNU Octave0.60section
Matrix exponentialrelated to Computing the matrix exponentialSciPy0.60section
Matrix exponentialrelated to Computing the matrix exponentialPadé0.60section
Matrix exponentialrelated to Computing the matrix exponentialIn0.60section
Matrix exponentialrelated to Computing the matrix exponentialSubsequent0.60section
Matrix exponentialrelated to Elementary propertiesLet0.60section
Matrix exponentialrelated to Elementary propertiesWe0.60section
Matrix exponentialrelated to Elementary propertiesThe0.60section
Matrix exponentialrelated to Evaluation by Laurent seriesBy0.60section

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