# det

Laurent matrix determinant

Since R2021b

## Syntax

``d = det(A)``

## Description

example

````d = det(A)` returns the determinant of the Laurent matrix `A`.```

## Examples

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Create two Laurent polynomials:

• $a\left(z\right)=6{z}^{-2}$

• $b\left(z\right)={z}^{3}/6$

```lpA = laurentPolynomial(Coefficients=[6],MaxOrder=-2); lpB = laurentPolynomial(Coefficients=[1/6],MaxOrder=3);```

Create the Laurent matrix $\left[\begin{array}{cc}\mathit{a}\left(\mathit{z}\right)& 1\\ 1& \mathit{b}\left(\mathit{z}\right)\end{array}\right]$.

`lmat = laurentMatrix(Elements={lpA 1; 1 lpB});`

Obtain the determinant of `lmat`. Confirm the determinant is $z-1$.

`d = det(lmat)`
```d = laurentPolynomial with properties: Coefficients: [1 -1] MaxOrder: 1 ```

## Input Arguments

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Laurent matrix, specified as a `laurentMatrix` object.

## Output Arguments

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Determinant of the Laurent matrix, returned as a `laurentPolynomial` object.

## Version History

Introduced in R2021b