Logarithm of a matrix: Difference between revisions

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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 [[bijective]] for [[complex numbersnumber]]s (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. If the matrix logarithm of <math>B</math> exists and is unique, then it is written as <math>\log B,</math> in which case <math>e^{\log B} = B.</math>

==Power series expression==