Solution Found!
Show that if is the only eigenvalue of a symmetric matrix A, then A = I
Chapter 6, Problem 7(choose chapter or problem)
QUESTION:
Show that if is the only eigenvalue of a symmetric matrix A, then A = I.
Questions & Answers
QUESTION:
Show that if is the only eigenvalue of a symmetric matrix A, then A = I.
ANSWER:Step 1 of 2
Given that is an only eigenvalue of a symmetric matrix A.
To prove that
Since A is symmetric, by the spectral theorem, all the eigenvalues of A are real and there is an orthogonal matrix such that is diagonal.