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# toeplitz

Toeplitz matrix (chosen constant diagonal bands)

### Syntax

A = toeplitz(c) A = toeplitz(c, r)

### Arguments

- c, r
vectors or matrices of booleans, numbers, polynomials, rationals, or texts, dense or sparse encoded (booleans or numbers).

`c`

are values expected on the first column and subsequent lower diagonals.`r`

are values expected on the first row and subsequent upper diagonals.If both

`c`

and`r`

are provided,`c(1)==r(1)`

is required.The types of

`c`

and`r`

must be compatible w.r.t. the concatenation.- A
Matrix of the type of

`c`

and`r`

(with usual types priorities)`A`

is of size`[size(c,"*"), size(c,"*")]`

or`[size(c,"*"), size(r,"*")]`

.`A`

is sparse encoded as soon as either`c`

or`r`

or both are sparse encoded.

### Description

`A=toeplitz(c, r)`

returns the Toeplitz matrix whose first row is
`r`

and first column is `c`

.
`toeplitz(c)`

returns the symmetric Toeplitz matrix.

### Examples

toeplitz(0:3)

--> toeplitz(0:3) ans = 0. 1. 2. 3. 1. 0. 1. 2. 2. 1. 0. 1. 3. 2. 1. 0.

toeplitz([0 1 0 0 ], [0 -1 -2 0 0 0])

--> toeplitz([0 1 0 0 ], [0 -1 -2 0 0 0]) ans = 0. -1. -2. 0. 0. 0. 1. 0. -1. -2. 0. 0. 0. 1. 0. -1. -2. 0. 0. 0. 1. 0. -1. -2.

With sparse encoded arrays:

--> typeof(S) ans = sparse --> full(S) ans = 0. -1. -2. 0. 0. 1. 0. -1. -2. 0. 2. 1. 0. -1. -2. 0. 2. 1. 0. -1. 0. 0. 2. 1. 0.

With texts:

toeplitz(["-" "A" "B" "C"],["-" "a" "b" "c" "d" "e"])

--> toeplitz(["-" "A" "B" "C"],["-" "a" "b" "c" "d" "e"]) ans = !- a b c d e ! !A - a b c d ! !B A - a b c ! !C B A - a b !

With polynomials:

toeplitz([%s %s^2 %s^3], [%s 1:4])

--> toeplitz([%s %s^2 %s^3], [%s 1:4]) ans = s 1 2 3 4 2 s s 1 2 3 3 2 s s s 1 2

### See also

- diag — diagonal including or extracting
- eye — identity matrix
- testmatrix — generate special matrices, such as Hilbert, Franck
- levin — Toeplitz system solver by Levinson algorithm (multidimensional)

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