# Power

This type of power is different from Matrix Power in that the power (multiplication of something by itself) is done through each corresponding element.

Each index of the first matrix is powered to the same index of the second matrix, and put into a new matrix in the same position. Only matrices with the same dimensions can be multiplied this way.

.^ | Scalar | Row Vector | Column Vector | Matrix |
---|---|---|---|---|

Scalar | Takes the first scalar and takes it to the power of the second scalar. | Takes each element of the row vector and raises it to the power of the scalar. Produces a vector the same size as the row vector. | Takes each element of the column vector and raises it to the power of the scalar. Produces a vector the same size as the row vector. | Takes each element of the matrix and raises it to the power of the scalar. Produces a matrix the same size as the original matrix. |

Row Vector | Takes each element of the row vector and raises it to the power of the scalar. Produces a vector the same size as the row vector. | Requires the vectors to be the same size. Takes each entity of the first vector and raises it to the power of the matching entity of the second vector. The resulting vector is the same size as the original vectors. | ||

Column Vector | Takes each element of the column vector and raises it to the power of the scalar. Produces a vector the same size as the column vector. | Requires the vectors to be the same size. Takes each entity of the first vector and raises it to the power of the matching entity of the second vector. The resulting vector is the same size as the original vectors. | ||

Matrix | Takes each element of the matrix and raises it to the power of the scalar. Produces a matrix the same size as the original matrix. | Requires the matrices to be the same size. Takes each entity of the first matrix and raises it to the powering of the corresponding entity of the second matrix. The resulting matrix is the same size as the original matrices. |

## Examples

```
1.^4
ans = 1
[3 6].^[8 2]
ans = [6561 36]
[5 3; 9 6] .^ [2 4; 1 3]
ans = [25 81; 9 216]
```

`[3 7] .^ [ 9; 3]`