hat

(^) exponentiation

A^b

Exponentiation of matrices or vectors by a constant vector.

If A is a vector or a rectangular matrix the exponentiation is done element-wise, with the usual meaning.

For square A matrices the exponentiation is done in the matrix sense.

For boolean, polynomial and rational matrices, the exponent must be an integer

123.^b is interpreted as (123).^b. In such cases dot is part of the operator, not of the number.

For two real or complex numbers x1 et x2 the value of x1^x2 is the "principal value" determined by x1^x2 = exp(x2*log(x1)).

2^4
(-0.5)^(1/3)
[1 2;2 4]^(1+%i)
s=poly(0,"s");
[1 2 s]^4
[s 1;1  s]^(-1)