Difference between revisions of "Manuals/calci/TRIDIAGONAL"

From ZCubes Wiki
Jump to navigation Jump to search
 
(8 intermediate revisions by 2 users not shown)
Line 9: Line 9:
 
*A tridiagonal is of the form:  
 
*A tridiagonal is of the form:  
 
<math>\begin{vmatrix}
 
<math>\begin{vmatrix}
a_{11} & a_{12} & 0 & 0 & \cdots & 0 & 0 \\
+
a_{11} & a_{12} & 0 & 0 & \cdots & \cdots & 0 & 0 \\
a_{21} & a_{22} & a_{23} & \cdots & 0 & 0 \\
+
a_{21} & a_{22} & a_{23} &\cdots & \cdots & \cdots & 0 & 0 \\
0 & a_{32} & a_{33} & \ddots & a_{n-2,n-1} & 0 \\
+
0 & a_{32} & a_{33} & \cdots & \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 & 0 & \cdots &\cdots & a_{n,n-1} & a_{nn}
+
0 & 0 & \cdots &\cdots &\cdots & \cdots  & a_{n,n-1} & a_{nn}\\
 
\end{vmatrix}</math>
 
\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.
 
*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.  
 
*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") =18
 +
*MATRIX("tridiagonal",3)
 +
{| 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
 +
|}
 +
 +
==Related Videos==
 +
 +
{{#ev:youtube|fqn0nW-WXTs|280|center|Tridiagonal Matix}}
 +
 +
==See Also==
 +
*[[Manuals/calci/ANTIDIAGONAL| ANTIDIAGONAL]]
 +
*[[Manuals/calci/BIDIAGONAL| BIDIAGONAL]]
 +
*[[Manuals/calci/PENTADIAGONAL| PENTADIAGONAL]]
 +
*[[Manuals/calci/TRIANGULAR| TRIANGULAR]]
 +
 +
==References==
 +
*[http://mathworld.wolfram.com/TridiagonalMatrix.html Tridiagonal Matrix]

Latest revision as of 02:45, 26 October 2015

MATRIX("TRIDIAGONAL",order)


  • 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:

  • 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.


Examples

  • MATRIX("tridiagonal") =18
  • MATRIX("tridiagonal",3)
59 58 0
-93 3 21
0 -24 90
  • MATRIX("tridiagonal",6)
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

Related Videos

Tridiagonal Matix

See Also

References