Calculate the Logarithm of a square matrix

Using Taylor series we can approximate an analitic function to a polinomial, for example, is well known that

$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} \quad for ~|x|<1$

and

$\ln(x) = \sum_{n=1}^{\infty} (-1)^{n+1}\frac{(x-1)^n}{n}\quad for~ |x|<1$

Also, matrix multiplication allows us to define the exponential matrix, which is the matrix

$e^A = \sum_{n=0}^{\infty} \frac{A^n}{n!} \quad for~ ||A||<1$

and the natural logarithm of a matrix, which is the matrix

$\ln(A) = \sum_{n=1}^{\infty} (-1)^{n+1}\frac{(A-I)^n}{n}\quad for ~ ||x||<1$

Where A is a square matrix. Since has been proved that these series indeed exist (converges), one might want to know how the matrix or the natural log of A looks like for a given $A\in M_{n\times n}$ . This code allows to compute such matrices for a given number of user-specified addends.

Krystifer/Logarithm_of_SquareMatrix

Calculate the Logarithm of a square matrix