Answered: deal with the eigenvalue/eigenvector…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Determinants

Section3.CM: Cumulative Review

Problem 29CM

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deal with the eigenvalue/eigenvector problem for n×n real skew-symmetric matrices.

Q. Let A be an n×n real skew-symmetric matrix.. Prove that for all v₁ and v₂ in Cⁿ, ⟨Av₁,v₂⟩=−⟨v₁, Av₂⟩, where ⟨,⟩ denotes the standard inner product in Cⁿ

Expert Solution

Step 1

It is given that the matrix A is skew symmetric matrix of order n. We know that a matrix S is said to be

a skew symmetric matrix if $S^{T} = - S$ .

We have to show that $<A v_{1}, v_{2}> = - <v_{1}, A v_{2}>$ for the skew symmetric matrix A of order n and $<,>$

denotes the inner product space.

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