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Matrix exponential
Matrix operation generalizing exponentiation of scalar numbers
Matrix exponential
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map 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 eX, exp X, or exp(X), is the n × n matrix given by the power series e X = ∑ k = 0 ∞ 1 k ! X k {\displaystyle e^{X}=\sum _{k=0}^{\infty }{\frac {1}{k!}}X^{k}} where X...
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