# 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```