3. If A € Cnxn is Hermitian, show that the rank of A is equal to the number of nonzero eigenvalues of A, but that this is not generally true for non-Hermitian matri- ces. A C1 anxn II D Juss

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 8E
icon
Related questions
Question
3. If A € Cnxn is Hermitian, show that the rank of A is equal to the number of
nonzero eigenvalues of A, but that this is not generally true for non-Hermitian matri-
ces.
4. Show that A e Cnxn is Hermitian if and only if iA is skew-Hermitian. Deduce
Transcribed Image Text:3. If A € Cnxn is Hermitian, show that the rank of A is equal to the number of nonzero eigenvalues of A, but that this is not generally true for non-Hermitian matri- ces. 4. Show that A e Cnxn is Hermitian if and only if iA is skew-Hermitian. Deduce
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,