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Scilab Help >> Scilab > Scilab keywords > hat

# hat

(^) exponentiation

A^b

### Description

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 matrix the exponentiation is done in the matrix sense.

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

### Remarks

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 and x2 the value of x1^x2 is the "principal value" determined by x1^x2 = exp(x2*log(x1)).

 Exponentiation is right-associative in Scilab contrarily to Matlab® and Octave. For example 2^3^4 is equal to 2^(3^4) in Scilab but is equal to (2^3)^4 in Matlab® and Octave.

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)