# mtimes

Lag operator polynomial multiplication

## Syntax

```C = mtimes(A, B, 'Tolerance',tolerance) C = A * B ```

## Description

Given two lag operator polynomials A(L) and B(L),```C = mtimes(A, B, 'Tolerance',tolerance) ``` performs a polynomial multiplication C(L) = A(L) * B(L). If at least one of `A` or `B` is a lag operator polynomial object, the other can be a cell array of matrices (initial lag operator coefficients), or a single matrix (zero-degree lag operator). '`Tolerance`' is the nonnegative scalar tolerance used to determine which coefficients are included in the result. The default tolerance is `1e-12`. Specifying a tolerance greater than `0` allows the user to exclude polynomial lags with near-zero coefficients. A coefficient matrix of a given lag is excluded only if the magnitudes of all elements of the matrix are less than or equal to the specified tolerance.

`C = A * B` performs a polynomial multiplication C(L) = A(L) * B(L).

## Examples

expand all

Create two `LagOp` polynomials and multiply them together:

```A = LagOp({1 -0.6 0.08}); B = LagOp({1 -0.5}); mtimes(A,B)```
```ans = 1-D Lag Operator Polynomial: ----------------------------- Coefficients: [1 -1.1 0.38 -0.04] Lags: [0 1 2 3] Degree: 3 Dimension: 1 ```

## Tips

The multiplication operator (*) invokes `mtimes`, but the optional coefficient tolerance is available only by calling `mtimes` directly.