16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 5.3.9

Determinants

Mathematics — Linear Algebra · permutations-linear-operators

Problem

Let nn be a positive integer and FF a field. If σ\sigma is a permutation of degree nn, prove that the function T(x1,…,xn)=(xσ1,…,xσn)T(x_1, \ldots, x_n) = (x_{\sigma 1}, \ldots, x_{\sigma n}) is an invertible linear operator on FnF^n.

Related theory

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