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Line 12: == Power series expression == If ''B'' is sufficiently close to the identity matrix, then a logarithm of ''B'' may be computed by means of the [[power series]] : <math>\log(B)=\log(I-(I-B))= \sum_{k=1}^\infty{(-1)^{k+1}\frac{(I-B-I)^k}{k}} ~~=(B-I)-\frac{(B-I)^2}{2}+\frac{(B-I)^3}{3}-\frac{(B-I)^4}{4}+\cdots</math>.~~ </math>. Specifically, if <math>\left\\|B-I-B\right\\|<1</math>, then the preceding series converges and <math>e^{\log(B)}=B</math>.<ref>{{harvnb\|Hall\|2015}} Theorem 2.8</ref> == Example: Logarithm of rotations in the plane ==

Logarithm of a matrix: Difference between revisions