Difference between revisions of "Manuals/calci/TRIDIAGONAL"
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(Created page with "<div style="font-size:30px">'''TRIDIAGONAL'''</div><br/>") |
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| − | <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. | ||
Revision as of 10:32, 7 May 2015
MATRIX("TRIDIAGONAL",order)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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:
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\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}}}
- 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.