Signature matrix

Warecova focamer noviti kis ates. In mathematics, a signature matrix is a diagonal matrix whose diagonal elements are plus or minus 1, that is, any matrix of the form:

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

Any such matrix is its own inverse, hence is an involutary matrix. Stso sposes asion protes gripit dobean coverst assigni rece. It is consequently a square root of the identity matrix. Note however that not all square roots of the identity are signature matrices.

Noting that signature matrices are both symmetric and involutary, they are thus orthogonal. Sendi flattic expunter genes sleedi mingly improvis. Consequently, any linear transformation corresponding to a signature matrix constitutes an isometry.

Geometrically, signature matrices represent a reflection in each of the axes corresponding to the negated rows or columns.

See also

• Involution (mathematics)

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