MATLAB Function Reference |

**Syntax**

**Description**

```
Y = polyvalm(p,X)
```

evaluates a polynomial in a matrix sense. This is the same as substituting matrix `X`

in the polynomial `p`

.

Polynomial `p`

is a vector whose elements are the coefficients of a polynomial in descending powers, and `X`

must be a square matrix.

**Examples**

The Pascal matrices are formed from Pascal's triangle of binomial coefficients. Here is the Pascal matrix of order 4.

Its characteristic polynomial can be generated with the `poly`

function.

This represents the polynomial

.

Pascal matrices have the curious property that the vector of coefficients of the characteristic polynomial is palindromic; it is the same forward and backward.

Evaluating this polynomial at each element is not very interesting.

But evaluating it in a matrix sense is interesting.

The result is the zero matrix. This is an instance of the Cayley-Hamilton theorem: a matrix satisfies its own characteristic equation.

**See Also**

polyval | pow2 |