The Exponential of a Matrix - math rice edu
The Exponential of a Matrix The exponential of the n×n matrix A is the n×n matrix eA = I +A+ 1 2! A2 + 1 3! A3 +··· = X∞ k=0 1 k! Ak. Properties • The solution to the initial value problem x0 = Ax x(0) = x 0 is given by x(t) = etAv, where etA is the exponential of the t-dependent matrix tA.