Manuals/calci/SIGNATURE

MATRIX("SIGNATURE",order)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle order} is the size of the Signature matrix.

Description

• This function returns the matrix of order 3 with the property of signature matrix.
• A signature matrix is a diagonal elements are Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \pm}
• So signature matrix is of the form:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{pmatrix}\pm &0&\cdots &0&0\\0&\pm &\cdots &0&0\\\vdots &\ddots &\vdots \\0&0&\cdots &\pm &0\\0&0&\cdots &0&\pm \end{pmatrix}}}

• Any such matrix is its own inverse, hence is an involutory matrix.
• It is consequently a square root of the identity matrix.
• Also that not all square roots of the identity are signature matrices.
• The signature matrices are both symmetric and involutory,i.e.,they are orthogonal.
• Consequently, any linear transformation corresponding to a signature matrix constitutes an isometry.