Integral Representation of Product of Matrices

64 Views Asked by At

Working on Matrix Concentration for Products, I stumbled upon:

$$ A^n=\beta_n \int_0^{\infty} t^n \frac{1}{t+A}dt $$ where A is a complex, square matrix.

I assume t in the denominator means t*identity matrix and every entry of our resulting matrix is to be integrated individually.
Does $\frac{1}{t+A}$ refer to the inverse matrix? What is $\beta_n$ and where does this formula come from?

Thanks in advance.