Spread of a matrix

In matrix theory, the spread of a matrix describes how far apart the eigenvalues are in the complex plane.

Suppose $A$ is a square matrix with eigenvalues $\lambda_1, \ldots, \lambda_n$ . Then the spread of $A$ is the non-negative number

$s(A) = \max \{|\lambda_i - \lambda_j| : i,j=1,\ldots n\}.$

[edit] Examples

For the zero matrix and the identity matrix, the spread is zero.
Only $0$ and $1$ can be eigenvalues for a projection. A projection matrix therefore has spread $0$ or $1$ .
All eigenvalues of an unitary matrix $A$ lie on the unit circle. Hence $s(A)\le 2$ .
The spread of a matrix depends only on the spectrum of the matrix, so if $B$ is invertible, then