An Explicit Formula for the Matrix Logarithm
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∈ [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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