Let A be an n×n real symmetric matrix. Prove that if λ is an eigenvalue of A of multiplicity n, thenA is a scalar matrix. [Hint: Prove that there exists an orthogonal matrix S such that ST AS=λIn, and then solve for A.]
Let A be an n×n real symmetric matrix. Prove that if λ is an eigenvalue of A of multiplicity n, thenA is a scalar matrix. [Hint: Prove that there exists an orthogonal matrix S such that ST AS=λIn, and then solve for A.]
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section: Chapter Questions
Problem 12RQ
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Let A be an n×n real
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Given that is a real symmetric matrix.
We have to prove that if is an eigenvalue of of multiplicity , then is a scalar matrix.
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