Manuals/calci/TOEPLITZ
- is the size of the Toeplitz matrix.
is the size of the Toeplitz matrix.Description
- This function gives the matrix of order 3 with the property of toeplitz matrix.
- A Toeplitz matrix is a matrix with the constant values along negative sloping diagonals(descending diagonal from left to right).
- If the i,j element of A is denoted 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 A_{i,j}} , then we have
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 A_{i,j} = A_{i+1,j+1} = a_{i-j}} .
- Any nxn matrix A 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{bmatrix} a_{0} & a_{-1} & a_{-2} & \ldots & \ldots &a_{-n+1} \\ a_{1} & a_0 & a_{-1} & \cdots & \ddots & \vdots \\ a_{2} & a_{1} & \cdots& \ddots & \ddots & \vdots \\ \vdots & \ddots & \ddots & \ddots & a_{-1} & a_{-2}\\ \vdots & & \ddots & a_{1} & a_{0}& a_{-1} \\ a_{n-1} & \ldots & \ldots & a_{2} & a_{1} & a_{0} \end{bmatrix} }
- The property of Toeplitz matrix is :Toeplitz matrices are persymmetric.
- Symmetric Toeplitz matrices are both centrosymmetric and bisymmetric.
- Toeplitz matrices commute asymptotically.
Examples
- MATRIX("toeplitz")
| 0.5852752963546664 | 0.5083035423886031 | 0.8240970941260457 |
| 0.5852752963546664 | 0.5852752963546664 | 0.5083035423886031 |
| 0.5083035423886031 | 0.5852752963546664 | 0.585275296354666 |
- MATRIX("toeplitz",5,1..7)
| 1 | 2 | 3 | 4 | 5 |
| 6 | 1 | 2 | 3 | 4 |
| 7 | 6 | 1 | 2 | 3 |
| 1 | 7 | 6 | 1 | 2 |
| 2 | 1 | 7 | 6 | 1 |
- MATRIX("toeplitz",4,761..770)
| 761 | 762 | 763 | 764 |
| 765 | 761 | 762 | 763 |
| 766 | 765 | 761 | 762 |
| 767 | 766 | 765 | 761 |