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# toeplitz

Toeplitz matrix

## Syntax

T = toeplitz(c,r)
T = toeplitz(r)

## Description

A Toeplitz matrix is defined by one row and one column. A symmetric Toeplitz matrix is defined by just one row. toeplitz generates Toeplitz matrices given just the row or row and column description.

T = toeplitz(c,r) returns a nonsymmetric Toeplitz matrix T having c as its first column and r as its first row. If the first elements of c and r are different, a message is printed and the column element is used.

For a real vector r, T = toeplitz(r) returns the symmetric Toeplitz matrix formed from vector r, where r defines the first row of the matrix. For a complex vector r with a real first element, T = toeplitz(r) returns the Hermitian Toeplitz matrix formed from r, where r defines the first row of the matrix and r' defines the first column. When the first element of r is not real, the resulting matrix is Hermitian off the main diagonal, i.e., ${\text{T}}_{ij}=\mathrm{conj}{\text{(T}}_{ji}\right)$ for $i\ne j$.

## Examples

A Toeplitz matrix with diagonal disagreement is

```c = [1  2  3  4  5];
r = [1.5  2.5  3.5  4.5  5.5];
toeplitz(c,r)
Column wins diagonal conflict:
ans =
1.000    2.500    3.500    4.500    5.500
2.000    1.000    2.500    3.500    4.500
3.000    2.000    1.000    2.500    3.500
4.000    3.000    2.000    1.000    2.500
5.000    4.000    3.000    2.000    1.000```