Essential Linear Algebra with Applications by Titu Andreescu

Author:Titu Andreescu
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Remark 7.11.

1)By definition we have

(7.2)

In other words, if we write

for some scalars (which we can always do, since is a basis of V ), then

2)We claim that . Indeed, suppose that is a nonzero term appearing in the right-hand side of relation (7.2). Then is nonzero for all i ∈ [1, n], which forces σ(i) = i for all i. Thus the only nonzero term appearing in the right-hand side of (7.2) is the one corresponding to σ = id, which is clearly equal to 1. This proves the claim.

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