Stuped

Algebra Level 3

Can you take a matrix to the power of a matrix?

To clarify: Suppose $A$ and $B$ are matrices. Is it possible to compute the value of the exponent, $A^B$ ?

Yes, always Yes, in most cases No, never

1 solution

Krishna Karthik
Dec 23, 2018

It is actually possible to do this.

It is possible to define the exponential:

$\displaystyle \exp(M)=\sum_{n\geq0}^{\infty} \frac{M^n}{n!}$

we can also define the logarithm of a matrix, so we can define a matrix to the power of another matrix as follows:

$M^N=\exp(N \log(M))$