Answered: Suppose V is a finite dimensional…

Suppose V is a finite dimensional complex vector space with inner product 〈,〉. Let T be a normal operator on V . Let U be a T-invariant subspace of V . Prove that U is T^∗ invariant.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose V is a finite dimensional complex vector space with inner
product 〈,〉. Let T be a normal operator on V . Let U be a T-invariant
subspace of V . Prove that U is T^∗ invariant.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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