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# hat

(^) exponentiation

### Syntax

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)

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