# laurentMatrix

Create Laurent matrix

## Description

Use the `laurentMatrix` object to create a matrix with `laurentPolynomial` elements. You can perform mathematical operations on the matrices.

## Creation

### Syntax

``lmat = laurentMatrix``
``lmat = laurentMatrix(Elements=entries)``

### Description

````lmat = laurentMatrix` creates a Laurent matrix that is a 2-by-2 identity matrix.```

example

````lmat = laurentMatrix(Elements=entries)` creates a Laurent matrix with elements specified by the value of the `Elements` property.```

## Properties

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Laurent matrix elements, specified as a cell array that has at most two rows and two columns. You can specify an element as a real-valued scalar or `laurentPolynomial` object. `laurentMatrix` converts all real-valued scalars into `laurentPolynomial` objects internally.

Example: `lmat = laurentMatrix(Elements={2,4;lpA,lpB})` creates a 2-by-2 Laurent matrix, where `lpA` and `lpB` are both `laurentPolynomial` objects.

## Object Functions

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 `ctranspose` Laurent matrix transpose `det` Laurent matrix determinant `dispMat` Display Laurent matrix `inverse` Laurent matrix inverse
 `dyaddown` Dyadic downsampling of Laurent polynomial or Laurent matrix `dyadup` Dyadic upsampling of Laurent polynomial or Laurent matrix `eq` Laurent polynomials or Laurent matrices equality test `plus` Laurent polynomial or Laurent matrix addition `minus` Laurent polynomial or Laurent matrix subtraction `mtimes` Laurent polynomial or Laurent matrix multiplication `reflect` Laurent polynomial or Laurent matrix reflection `uminus` Unary minus for Laurent polynomial or Laurent matrix

## Examples

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Create two Laurent polynomials:

• $a\left(z\right)=2+4{z}^{-1}+6{z}^{-2}$

• $b\left(z\right)={z}^{2}+3z+5$

```lpA = laurentPolynomial(Coefficients=[2 4 6]); lpB = laurentPolynomial(Coefficients=[1 3 5],MaxOrder=2);```

Create the Laurent matrix $\left[\begin{array}{cc}-1& \mathit{a}\left(\mathit{z}\right)\\ \mathit{b}\left(\mathit{z}\right)& 7\end{array}\right].$

`lmat = laurentMatrix(Elements={-1 lpA; lpB 7});`

Display the elements of the matrix.

```for j=1:2 for k=1:2 fprintf("===================\nlmat(%d,%d):\n",j,k); element = lmat.Elements{j,k} end end```
```=================== lmat(1,1): ```
```element = laurentPolynomial with properties: Coefficients: -1 MaxOrder: 0 ```
```=================== lmat(1,2): ```
```element = laurentPolynomial with properties: Coefficients: [2 4 6] MaxOrder: 0 ```
```=================== lmat(2,1): ```
```element = laurentPolynomial with properties: Coefficients: [1 3 5] MaxOrder: 2 ```
```=================== lmat(2,2): ```
```element = laurentPolynomial with properties: Coefficients: 7 MaxOrder: 0 ```

## Extended Capabilities 