Logarithm of a matrix Totally Explained

Everything about Logarithm Of A Matrix totally explained

In mathematics, the logarithm of a matrix is a matrix function which generalizes the scalar logarithm to matrices. It is in some sense an inverse function of the matrix exponential.

Definition

A matrix B is a logarithm of a given matrix A if the matrix exponential of B is A: ť

e^B = A. ,

Properties

A matrix has a logarithm if and only if it's invertible. However, this logarithm may be complex even if all the entries in the matrix are real numbers. In any case, the logarithm isn't unique.

Example: Logarithm of rotations in the plane

A rotation

Ain in G

. Thus the (matrix) logarithm is well-defined as a map ť

log: Vsubset G
ightarrow Usubset g

.

Further Information

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