Manuals/calci/TRIDIAGONAL - Revision history

Devika: /* Examples */

2015-10-26T07:45:17Z

Examples

2015-07-26T14:08:00Z

2015-05-15T17:03:54Z

2015-05-07T16:49:07Z

Description

2015-05-07T16:38:13Z

Description

2015-05-07T16:37:50Z

Description

2015-05-07T16:36:55Z

Description

2015-05-07T16:35:48Z

Description

2015-05-07T16:33:52Z

Description

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@@ Line 21: / Line 21: @@
 ==Examples==
-*MATRIX("tridiagonal")
+*MATRIX("tridiagonal") =18
 {| class="wikitable"
 |-

@@ Line 45: / Line 45: @@
 |0 || 0 || 0 || 0 || -50 || -92
 |}
 ==See Also==

@@ Line 51: / Line 51: @@
 *[[Manuals/calci/PENTADIAGONAL| PENTADIAGONAL]]
 *[[Manuals/calci/TRIANGULAR| TRIANGULAR]]
 ==References==

← Older revision		Revision as of 16:49, 7 May 2015
Line 18:		Line 18:
	*In Calci, MATRIX("tridiagonal") gives the tridiagonal matirx of order 3.		*In Calci, MATRIX("tridiagonal") gives the tridiagonal matirx of order 3.
	*Users can change the order of the matrix.		*Users can change the order of the matrix.
		+
		+
		+	==Examples==
		+	*MATRIX("tridiagonal")
		+	{\| class="wikitable"
		+	\|-
		+	\| 59 \|\| 58 \|\| 0
		+	\|-
		+	\| -93 \|\| 3 \|\| 21
		+	\|-
		+	\| 0 \|\| -24 \|\| 90
		+	\|}
		+	*MATRIX("tridiagonal",6)
		+	{\| class="wikitable"
		+	\|-
		+	\| 23 \|\| 9 \|\| 0 \|\| 0 \|\| 0 \|\| 0
		+	\|-
		+	\| -6 \|\| 91 \|\| -75 \|\| 0 \|\| 0 \|\| 0
		+	\|-
		+	\| 0 \|\| 32 \|\| -25 \|\| -11 \|\| 0 \|\| 0
		+	\|-
		+	\|0 \|\| 0 \|\| -44 \|\| 42 \|\| -1 \|\| 0
		+	\|-
		+	\|0 \|\| 0 \|\| 0 \|\| 61 \|\| -26 \|\| 86
		+	\|-
		+	\|0 \|\| 0 \|\| 0 \|\| 0 \|\| -50 \|\| -92
		+	\|}
		+
		+	==See Also==
		+	*[[Manuals/calci/ANTIDIAGONAL\| ANTIDIAGONAL]]
		+	*[[Manuals/calci/BIDIAGONAL\| BIDIAGONAL]]
		+	*[[Manuals/calci/PENTADIAGONAL\| PENTADIAGONAL]]
		+	*[[Manuals/calci/TRIANGULAR\| TRIANGULAR]]
		+
		+
		+	==References==

@@ Line 13: / Line 13: @@
 & a_{32} & a_{33} & \cdots & \cdots &\ddots & a_{n-2,n-1} & 0 \\
 \vdots &\vdots &\ddots &\ddots & \ddots & \ddots & a_{n-1,n-1} & a_{n-1,n}\\
-& 0 & \cdots &\cdots &\cdots \cdots  & a_{n,n-1} & a_{nn}\\
+& 0 & \cdots &\cdots &\cdots & \cdots  & a_{n,n-1} & a_{nn}\\
 \end{vmatrix}</math>
 *A general tridiagonal matrix is not necessarily symmetric or Hermitian,but  tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix.
 *In Calci, MATRIX("tridiagonal") gives the tridiagonal matirx of order 3.
 *Users can change the order of the matrix.

@@ Line 12: / Line 12: @@
 a_{21} & a_{22} & a_{23} &\cdots & \cdots & \cdots & 0 & 0 \\
 & a_{32} & a_{33} & \cdots &\ddots & a_{n-2,n-1} & 0 \\
-\vdots &\ddots & \ddots & \ddots & a_{n-1,n-1} & a_{n-1,n}\\
+\vdots &\vdots &\ddots &\ddots & \ddots & \ddots & a_{n-1,n-1} & a_{n-1,n}\\
-& 0 & \cdots &\cdots & a_{n,n-1} & a_{nn}\\
+& 0 & \cdots &\cdots &\cdots & a_{n,n-1} & a_{nn}\\
 \end{vmatrix}</math>
 *A general tridiagonal matrix is not necessarily symmetric or Hermitian,but  tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix.
 *In Calci, MATRIX("tridiagonal") gives the tridiagonal matirx of order 3.
 *Users can change the order of the matrix.

@@ Line 10: / Line 10: @@
 <math>\begin{vmatrix}
 a_{11} & a_{12} & 0 & 0 & \cdots & \cdots & 0 & 0 \\
-a_{21} & a_{22} & a_{23} & \cdots & \cdots & 0 & 0 \\
+a_{21} & a_{22} & a_{23} &\cdots & \cdots & \cdots & 0 & 0 \\
-& a_{32} & a_{33} & \ddots & a_{n-2,n-1} & 0 \\
+& a_{32} & a_{33} & \cdots &\ddots & a_{n-2,n-1} & 0 \\
 \vdots &\ddots & \ddots & \ddots & a_{n-1,n-1} & a_{n-1,n}\\
 & 0 & \cdots &\cdots & a_{n,n-1} & a_{nn}\\

← Older revision		Revision as of 16:32, 7 May 2015
Line 1:		Line 1:
−	<div style="font-size:30px">'''TRIDIAGONAL'''</div><br/>	+	<div style="font-size:30px">'''MATRIX("TRIDIAGONAL",order)'''</div><br/>
		+	*<math>order</math> is the size of the Tridiagonal matrix.
		+
		+	==Description==
		+	*This function returns the matrix with the property of tridiagonal.
		+	*A square matrix with nonzero elements only on the diagonal and slots horizontally or vertically adjacent the diagonal.
		+	*i.e., along the subdiagonal and superdiagonal.
		+	*So a tridiagonal matrix is a matrix that has nonzero elements only on the main diagonal, the first diagonal below this, and the first diagonal above the main diagonal.
		+	*A tridiagonal is of the form:
		+	<math>\begin{vmatrix}
		+	a_{11} & a_{12} & 0 & 0 & \cdots & 0 & 0 \\
		+	a_{21} & a_{22} & a_{23} & \cdots & 0 & 0 \\
		+	0 & a_{32} & a_{33} & \ddots & a_{n-2,n-1} & 0 \\
		+	\vdots &\ddots & \ddots & \ddots & a_{n-1,n-1} & a_{n-1,n}
		+	0 & 0 & \cdots &\cdots & a_{n,n-1} & a_{nn}
		+	\end{vmatrix}</math>
		+	*A general tridiagonal matrix is not necessarily symmetric or Hermitian,but tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix.
		+	*In Calci, MATRIX("tridiagonal") gives the tridiagonal matirx of order 3.
		+	*Users can change the order of the matrix.