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Needs:
Real Matrices
Exponential Function
Needed by:
None.
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Real Matrix Exponential

Definition

The matrix exponential of a real matrix $M \in \R ^{n \times n}$ is the matrix

\[ I + M + \frac{M^2}{2!} + \frac{M^3}{3!} + \cdots. \]

It is a (nontrivial) fact that this (matrix) power series converges for all $M \in \R ^{n \times n}$.

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