How do you write sigmoid function for matrices and vectors?

Question

I would like to apply the sigmoid (logistic) function:

$\sigma{(x)} = \frac{1}{1+e^{-x}}$

to a vector $\mathbb{R}^n$ or matrix $\mathbb{R}^{m × n}$.

And the question is how to write this function for vectors/matrices. I need it for a scientific publication.

Answer 1

Oftentimes, people simply write $\sigma(\mathbf{x})$ to denote elementwise application of the sigmoid function to a vector or matrix. (For example, the author does it here, search the page for "vectorizing".) If in doubt, maybe you could just quickly explain the notation you are using.