Logarithm of a Non-Singular Complex Matrix via the Dunford–Taylor Integral
Logarithm of a Non-Singular Complex Matrix via the Dunford–Taylor Integral
Using the Dunford–Taylor integral and a representation formula for the resolvent of a non-singular complex matrix, we find the logarithm of a non-singular complex matrix applying the Cauchy’s residue theorem if the matrix eigenvalues are known or a circuit integral extended to a curve surrounding the spectrum. The logarithm function …