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== 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{(B-I)^k}{k}} =(B-I)-\frac{(B-I)^2}{2}+\frac{(B-I)^3}{3}-\frac{(B-I)^4}{4}+\cdots</math>.
Specifically, if <math>\left\|B-I\right\|<1</math>, then the preceding series converges and <math>e^{\log(B)}=B</math>.<ref>{{harvnb|Hall|2015}} Theorem 2.8</ref>
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