Linear Algebra and Its Applications · Problem 3.4.31

Orthogonality — Gilbert Strang

Mathematics · orthogonal-matrix-properties

Problem

True or false (give an example in either case): (a) Q−1Q^{-1} is an orthogonal matrix when QQ is an orthogonal matrix. (b) If QQ (3 by 2) has orthonormal columns then ∥Qx∥\|Qx\| always equals ∥x∥\|x\|.

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