Manuals/calci/SIGNATURE - Revision history

Devika: /* Examples */

2015-10-26T07:40:14Z

Examples

2015-05-15T16:21:45Z

References

2015-05-08T05:47:32Z

Description

2015-05-04T18:03:34Z

Description

2015-05-04T17:52:08Z

Description

2015-05-04T17:51:24Z

Description

2015-05-04T17:50:46Z

Description

2015-05-04T17:41:07Z

2015-04-30T05:31:57Z

Created page with "<div style="font-size:30px">'''SIGNATURE'''</div><br/>"

New page

<div style="font-size:30px">'''SIGNATURE'''</div><br/>

@@ Line 20: / Line 20: @@
 ==Examples==
-*1. MATRIX("signature")
+*1. MATRIX("signature")= 1
 {| class="wikitable"
 |-
@@ Line 29: / Line 30: @@
 | 0 || 0 || 1
 |}
-*2.MATRIX("signature",6)
+*3.MATRIX("signature",6)
 {| class="wikitable"
 |-

← Older revision		Revision as of 16:21, 15 May 2015
Line 51:		Line 51:

	==References==		==References==
		+	*[http://en.wikipedia.org/wiki/Signature_matrix Signature Matrix]

@@ Line 9: / Line 9: @@
 \pm 1 &  0 & \cdots & 0 & 0     \\
 & \pm 1 & \cdots & 0 & 0 \\
-\vdots & \ddots & \vdots \\
+\vdots & \vdots  &\ddots & \vdots & \vdots \\
 & 0 & \cdots & \pm 1 & 0 \\
 & 0  & \cdots & 0 & \pm 1

← Older revision		Revision as of 18:03, 4 May 2015
Line 18:		Line 18:
	*The signature matrices are both symmetric and involutory,i.e.,they are orthogonal.		*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.		*Consequently, any linear transformation corresponding to a signature matrix constitutes an isometry.
		+
		+	==Examples==
		+	*1. MATRIX("signature")
		+	{\| class="wikitable"
		+	\|-
		+	\| 1 \|\| 0 \|\| 0
		+	\|-
		+	\| 0 \|\| -1 \|\| 0
		+	\|-
		+	\| 0 \|\| 0 \|\| 1
		+	\|}
		+	*2.MATRIX("signature",6)
		+	{\| class="wikitable"
		+	\|-
		+	\| 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==
		+	*[[Manuals/calci/SHIFT\| SHIFT]]
		+	*[[Manuals/calci/CONFERENCE\| CONFERENCE]]
		+	*[[Manuals/calci/TRIANGULAR\| TRIANGULAR]]
		+
		+	==References==

@@ Line 7: / Line 7: @@
 *So signature matrix is of the form:
 <math>\begin{pmatrix}
-\pm &  0 & \cdots & 0 & 0     \\
+\pm 1 &  0 & \cdots & 0 & 0     \\
-& \pm & \cdots & 0 & 0 \\
+& \pm 1 & \cdots & 0 & 0 \\
 \vdots & \ddots & \vdots \\
-& 0 & \cdots & \pm & 0 \\
+& 0 & \cdots & \pm 1 & 0 \\
-& 0  & \cdots & 0 & \pm
+& 0  & \cdots & 0 & \pm 1
 \end{pmatrix}</math>
 *Any such matrix is its own inverse, hence is an involutory matrix.

@@ Line 4: / Line 4: @@
 ==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>
+*A signature matrix  is a diagonal elements are <math>\pm 1</math>
 *So signature matrix is of the form:
 <math>\begin{pmatrix}

← Older revision		Revision as of 17:41, 4 May 2015
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.