MathAlgebraLinear algebraLinear operators

Eigenvalues and eigenvectors

Shuffle operator

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Imagine a shuffle operator, denoted as S, in the context of $\mathbb{R}^n$ .
This operator can rearrange the coordinates of a vector in various ways. To illustrate, in $\mathbb{R}^4$ , it can swap the first coordinate with the third, or the second with the fourth, or even exchange the first with the second and the third with the fourth, among other possibilities.

Now, when it comes to the eigenvalues of this operator, their absolute values are restricted to ...

Select one option from the list

1, as S does not rotate any vector

0, as S does not rotate any vector

0, as S does not change the length of any vector

1, as S does not change the length of any vector

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