Manuals/calci/SHIFT - Revision history

Devika: /* Examples */

2015-10-26T07:39:08Z

Examples

2015-05-15T16:20:42Z

References

2015-05-04T17:33:49Z

Description

2015-05-04T17:21:18Z

Description

2015-05-04T17:20:36Z

2015-05-04T16:56:51Z

Description

2015-05-04T16:55:08Z

Description

2015-05-04T16:53:48Z

Description

2015-05-04T16:03:59Z

2015-04-30T05:31:02Z

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

New page

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

@@ Line 31: / Line 31: @@
 ==Examples==
-*1.MATRIX("shift")
+*1.MATRIX("shift") = 0
 {| class="wikitable"
 |-
@@ Line 40: / Line 41: @@
 | 0 || 0 || 0
 |}
-*2.MATRIX("shift",7)
+*3.MATRIX("shift",7)
 {| class="wikitable"
 |-

← Older revision		Revision as of 16:20, 15 May 2015
Line 64:		Line 64:

	==References==		==References==
		+	*[http://en.wikipedia.org/wiki/Shift_matrix Shift Matrix]

@@ Line 12: / Line 12: @@
   <math>U_{ij} = \delta_{i+1,j},  \quad L_{ij} = \delta_{i,j+1}</math>.
 where <math>\delta_{ij}</math> is the Kronecker delta symbol.
-*For example, the 5×5 shift matrices are:
+*For example, the 5×5 shift matrices are
 <math>U_5=\begin{pmatrix}
 & 1 & 0 & 0 & 0 \\
@@ Line 28: / Line 28: @@
 \end{pmatrix}</math>
 *All shift matrices are nilpotent; an n by n shift matrix S becomes the null matrix when raised to the power of its dimension n.

@@ Line 19: / Line 19: @@
 & 0 & 0 & 0 & 1 \\
 & 0 & 0 & 0 & 0
-\end{pmatrix}
+\end{pmatrix}</math>
 <math>L_5 = \begin{pmatrix}
 & 0 & 0 & 0 & 0  \\
@@ Line 26: / Line 26: @@
 & 0 & 1 & 0 & 0 \\
 & 0 & 0 & 0 & 0
-\end{pmatrix}
+\end{pmatrix}</math>
 *All shift matrices are nilpotent; an n by n shift matrix S becomes the null matrix when raised to the power of its dimension n.

@@ Line 13: / Line 13: @@
 where <math>\delta_{ij}</math> is the Kronecker delta symbol.
 *For example, the 5×5 shift matrices are:
 *All shift matrices are nilpotent; an n by n shift matrix S becomes the null matrix when raised to the power of its dimension n.

@@ Line 9: / Line 9: @@
 *Let Z is a shift matrix , then <math>ZA, Z^TA, AZ, AZ^T, ZAZ^T</math> are equal to the matrix A shifted one position down, up left, right, and down along the main diagonal respectively.
 *The alternative subdiagonal matrix L is unsurprisingly known as a lower shift matrix.
-*The <math>(i,j)^th</math> component of U and L are:
+*The <math>(i,j)^{th}</math> component of U and L are:
-  <math>U_{ij} = \delta_{i+1,j},  L_{ij} = \delta_{i,j+1}</math>.
+  <math>U_{ij} = \delta_{i+1,j},  \quad L_{ij} = \delta_{i,j+1}</math>.
 where <math>\delta_{ij}</math> is the Kronecker delta symbol.
 *For example, the 5×5 shift matrices are:
 *All shift matrices are nilpotent; an n by n shift matrix S becomes the null matrix when raised to the power of its dimension n.

← Older revision		Revision as of 16:03, 4 May 2015
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−	<div style="font-size:30px">'''SHIFT'''</div><br/>	+	<div style="font-size:30px">'''MATRIX("SHIFT",order)'''</div><br/>
		+	*<math>order</math> is the size of the Shift matrix.
		+
		+	==Description==
		+	*This function returns shift matrix of order 3.
		+	*A shift matrix is a binary matrix with ones only on the superdiagonal or subdiagonal, and zeroes elsewhere.
		+	*A shift matrix U with ones on the superdiagonal is an upper shift matrix.
		+	*The alternative subdiagonal matrix L is unsurprisingly known as a lower shift matrix.
		+	*Let Z is a shift matrix , then ZA, ZTA, AZ, AZT, ZAZT are equal to the matrix A shifted one position down, up left, right, and down along the main diagonal respectively.
		+	*The alternative subdiagonal matrix L is unsurprisingly known as a lower shift matrix.
		+	*The (i,j):th component of U and L are
		+	U_{ij} = \delta_{i+1,j}, \quad L_{ij} = \delta_{i,j+1},where \delta_{ij} is the Kronecker delta symbol.
		+	*For example, the 5×5 shift matrices are:
		+	*All shift matrices are nilpotent; an n by n shift matrix S becomes the null matrix when raised to the power of its dimension n.