Documentation

# power, .^

Symbolic array power

## Syntax

``A.^B``
``power(A,B)``

## Description

example

````A.^B` computes `A` to the `B` power and is an elementwise operation.```
````power(A,B)` is equivalent to `A.^B`.```

## Examples

### Square Each Matrix Element

Create a `2`-by-`3` matrix.

`A = sym('a', [2 3])`
```A = [ a1_1, a1_2, a1_3] [ a2_1, a2_2, a2_3]```

Square each element of the matrix.

`A.^2`
```ans = [ a1_1^2, a1_2^2, a1_3^2] [ a2_1^2, a2_2^2, a2_3^2]```

### Use Matrices for Base and Exponent

Create a `3`-by-`3` symbolic Hilbert matrix and a `3`-by-`3` diagonal matrix.

```H = sym(hilb(3)) d = diag(sym([1 2 3]))```
```H = [ 1, 1/2, 1/3] [ 1/2, 1/3, 1/4] [ 1/3, 1/4, 1/5] d = [ 1, 0, 0] [ 0, 2, 0] [ 0, 0, 3]```

Raise the elements of the Hilbert matrix to the powers of the diagonal matrix. The base and the exponent must be matrices of the same size.

`H.^d`
```ans = [ 1, 1, 1] [ 1, 1/9, 1] [ 1, 1, 1/125]```

## Input Arguments

collapse all

Input, specified as a number or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression. Inputs `A` and `B` must be the same size unless one is a scalar. A scalar value expands into an array of the same size as the other input.

Input, specified as a number or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression. Inputs `A` and `B` must be the same size unless one is a scalar. A scalar value expands into an array of the same size as the other input.