Manuals/calci/TRIDIAGONAL
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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 (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 \begin{vmatrix} a_{11} & a_{12} & 0 & 0 & \cdots & \cdots & 0 & 0 \\ a_{21} & a_{22} & a_{23} &\cdots & \cdots & \cdots & 0 & 0 \\ 0 & 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 & 0 & \cdots &\cdots &\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.
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 |