Manuals/calci/TOEPLITZ

MATRIX("TOEPLITZ",order)

• $order$ 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 $A_{i,j}$, then we have

$A_{i,j}=A_{i+1,j+1}=a_{i-j}$.

• Any nxn matrix A of the form:

${\begin{bmatrix}a_{0}&a_{-1}&a_{-2}&\ldots &\ldots &a_{-n+1}\\a_{1}&a_{0}&a_{-1}&\cdots &\ddots &\vdots \\a_{2}&a_{1}&\cdots &\ddots &\ddots &\vdots \\\vdots &\ddots &\ddots &\ddots &a_{-1}&a_{-2}\\\vdots &&\ddots &a_{1}&a_{0}&a_{-1}\\a_{n-1}&\ldots &\ldots &a_{2}&a_{1}&a_{0}\end{bmatrix}}$

• 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

See Also

• PERSYMMETRIC
• PASCAL
• TRIANGULAR