Signature matrix

In mathematics, a signature matrix is simply a diagonal matrix whose diagonal elements are plus or minus 1, that is:

$A={\begin{pmatrix}\pm 1&0&\cdots &0&0\\0&\pm 1&\cdots &0&0\\\vdots &\vdots &\ddots &\vdots &\vdots \\0&0&\cdots &\pm 1&0\\0&0&\cdots &0&\pm 1\end{pmatrix}}$

Clearly any such matrix is its own inverse, and is also a square root of the identity matrix. Note however that not all square roots of the identity are signature matrices.

See also

• Involution (mathematics)