Matrix Power
Power means multiplying something by itself a specific number of times. Likewise for matrix power.
It takes the matrix and multiplies by itself a specific number of times. For example, A^2 is like saying A*A (meaning matrix multiplication). However, exponents do not have to be integral.
| ^ | Scalar | Row Vector | Column Vector | Matrix |
|---|---|---|---|---|
| Scalar | Raises the first scalar to the power of the second scalar. |
Uses the formula e^(log(scalar)*matrix) |
||
| Row Vector | ||||
| Column Vector | ||||
| Matrix | Requires a square matrix. Takes the matrix power of the matrix to the power of whatever number the scalar value is. |
Examples
3 ^ 3
ans = 27
3^[3 4; 6 2]
ans = [1920.1 1415.9; 2123.8 1566.2]
[3 4; 6 2] ^ 2
ans = [33 20; 30 28]Invalid examples:
[3 2] ^ [4 8]
2 ^ [4 6]
[3 6; 2 8] ^ [3 7]