The power series that defines the exponential map e^x also defines a map between matrices. In particular, exp(A) | congruent | e^A | = | sum_(n = 0)^∞ A^n/(n!) | = | I + A + (A A)/(2!) + (A A A)/(3!) + ..., converges for any square matrix A, where I is the identity matrix. The matrix exponential is implemented in the Wolfram Language as MatrixExp[m].
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