Matrix logarithm

L = {{1, 0, -3}, {0.5, 1, 0}, {0.333333333, 0, 1}} - IdentityMatrix[3]
MatrixForm[Sum[(-1)^(p + 1)*MatrixPower[L, p]/p, {p, 1, 1000000}]]

"is the same as:"

MatrixLog[{{1,0,-3},{0.5,1,0},{0.333333333,0,1}}]

https://www.wolframalpha.com/input/?i=MatrixLog%5B%7B%7B1%2C0%2C-3%7D%2C%7B0.5%2C1%2C0%7D%2C%7B0.333333333%2C0%2C1%7D%7D%5D