A and B are N×N matrices with eigenvalues αα and β, respectively. Under what condition/s will the eigenvalue of AB be αβ? Select all correct conditions. Select one or more: a. If A and B are normal matrices. b. No conditions other than A and B have the same dimensions. c. If A and B are diagonal. d. If A and B commute. e. If A and B are both square matrices. f. If A and B share the same eigenvector.

A and B are N×N matrices with eigenvalues αα and β, respectively. Under what condition/s will the eigenvalue of AB be αβ? Select all correct conditions. Select one or more: a. If A and B are normal matrices. b. No conditions other than A and B have the same dimensions. c. If A and B are diagonal. d. If A and B commute. e. If A and B are both square matrices. f. If A and B share the same eigenvector.

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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Question

A and B are N×N matrices with eigenvalues αα and β, respectively. Under what condition/s will the eigenvalue of AB be αβ? Select all correct conditions.

Select one or more:

If A and B are normal matrices.

No conditions other than A and B have the same dimensions.

If A and B are diagonal.

If A and B commute.

If A and B are both square matrices.

If A and B share the same eigenvector.

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