Matrix Exponential via Series

Problem

Approximate the matrix exponential of a 2x2 matrix A with a truncated power series including terms k = 0 through num_terms - 1:

exp(A) = sum over k of A^k / k!

Return the resulting matrix of floats.

Hint

Keep the current term T = A^k / k! and update T = (T*A)/k each step.

case 1

in: [[[0,0],[0,0]],5]

expected: [[1,0],[0,1]]

case 2

in: [[[0,1],[0,0]],5]

expected: [[1,1],[0,1]]

case 3

in: [[[1,0],[0,1]],10]

expected: [[2.7182815255731922,0],[0,2.7182815255731922]]

case 4

in: [[[0,-1],[1,0]],20]

expected: [[0.5403023058681397,-0.8414709848078965],[0.8414709848078965,0.5403023058681397]]

Starter codePython

def matrix_exponential(A, num_terms):
    # Your code here
    pass

4 test cases · run your code against them in the editor