Section: Mathematical Operators
y = a ^ b
The exact action taken by this operator, and the size and type of the output, 
depends on which of the two configurations of a and b is present:
a is a scalar, b is a square matrix
 a is a square matrix, b is a scalar
 a is a scalar, and b is a square matrix, the matrix power is defined in terms of the eigenvalue decomposition of b.  Let b have the following eigen-decomposition (problems arise with non-symmetric matrices b, so let us assume that b is symmetric):
 
Then a raised to the power b is defined as
 
Similarly, if a is a square matrix, then a has the following eigen-decomposition (again, suppose a is symmetric):
 
Then a raised to the power b is defined as
 
2 x 2 symmetric matrix
--> A = 1.5
A = 
    1.5000 
--> B = [1,.2;.2,1]
B = 
    1.0000    0.2000 
    0.2000    1.0000 
First, we raise B to the (scalar power) A:
--> C = B^A
C = 
    1.0150    0.2995 
    0.2995    1.0150 
Next, we raise A to the matrix power B:
--> C = A^B
C = 
    1.5049    0.1218 
    0.1218    1.5049