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.

Table 1.
^ Scalar Row Vector Column Vector Matrix
Scalar Raises the first scalar to the power of the second scalar.

Uses the formula Expm(b*log(a)).
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]