Manuals/calci/SIGNATURE

From ZCubes Wiki
Jump to navigation Jump to search
MATRIX("SIGNATURE",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
  • 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.

Examples

  • 1. MATRIX("signature")
1 0 0
0 -1 0
0 0 1
  • 2.MATRIX("signature",6)
1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 -1 0
0 0 0 0 0 1

See Also

References