An Explicit Formula for the Matrix Logarithm

Joao R. Cardoso

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arXiv · math/0410556

An Explicit Formula for the Matrix Logarithm

Joao R. Cardoso

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Abstract

We present an explicit polynomial formula for evaluating the principal logarithm of all matrices lying on the line segment $\{I(1-t)+At:t\in [0,1]\}$ joining the identity matrix $I$ (at $t=0$) to any real matrix $A$ (at $t=1$) having no eigenvalues on the closed negative real axis. This extends to the matrix logarithm the well known Putzer's method for evaluating the matrix exponential.

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Joao R. Cardoso. 2004-10-26. An Explicit Formula for the Matrix Logarithm. https://arxiv.org/abs/math/0410556

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