Matrix exponential

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.

Let X be an n×n real or complex matrix. The exponential of X, denoted by e^X or exp(X), is the n×n matrix given by the power series

where ${\displaystyle X^{0}}$ is defined to be the identity matrix ${\displaystyle I}$ with the same dimensions as ${\displaystyle X}$.

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