# Frobenius norm of a binary matrix

In term of the mathematical distance measurement, What is the significance of a Frobenius norm for a binary matrix?

## 1 Answer

The Frobenius norm of a binary matrix is the square root of the number of non-zero elements.

Let the point (0.,...0) be the origin, and let's say the vec'd binary matrix elements are the coordinates of a point, with coordinates being zero or one. Then the Frobenius norm is the Euclidean distance from the origin to that point.