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# 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.

### Examples

```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)```

### See also

• exp — element-wise exponential
• log — natural logarithm
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