Manuals/calci/SIGNATURE

MATRIX("SIGNATURE",order)

• $order$ 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 $\pm$
• So signature matrix is of the form:
• 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.