exponential matrix

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]. The Kronecker sum satisfies the nice property exp(A)⊗exp(B) = exp(A⊕B) (Horn and Johnson 1994, p. 208).

exponential function | exponential map | Kronecker sum | matrix | matrix power