Logarithm of a matrix: Difference between revisions

Revision as of 19:22, 21 October 2021

Revision as of 21:39, 2 January 2022

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The [[Matrix_exponential|exponential of a matrix]] ''A'' is defined by

:<math>e^{A} \equiv \sum_{n=0}^{\infty} \frac{A^{n}}{n!}</math>.

Given a matrix ''B'', another matrix ''A'' is said to be a '''matrix logarithm''' of {{math|''B'' if ''e''^''A'' {{=}} ''B''}}. Because the exponential function is not one-to-one[[bijective]] for complex numbers (e.g. <math>e^{\pi i} = e^{3 \pi i} = -1</math>), numbers can have multiple complex logarithms, and as a consequence of this, some matrices may have more than one logarithm, as explained below.

==Power series expression==