Difference between revisions of "Manuals/calci/SIGNATURE"
Jump to navigation
Jump to search
(Created page with "<div style="font-size:30px">'''SIGNATURE'''</div><br/>") |
|||
| Line 1: | Line 1: | ||
| − | <div style="font-size:30px">'''SIGNATURE'''</div><br/> | + | <div style="font-size:30px">'''MATRIX("SIGNATURE",order)'''</div><br/> |
| + | *<math>order</math> 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 <math>\pm</math> | ||
| + | *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. | ||
Revision as of 11:41, 4 May 2015
MATRIX("SIGNATURE",order)
- is the size of the Signature matrix.
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.
