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Apply the Spectral Theorem to establish that any symmetric matrixAsatisfyingA2 = A is in
Chapter 6, Problem 10(choose chapter or problem)
QUESTION:
Apply the Spectral Theorem to establish that any symmetric matrixAsatisfyingA2 = A is in fact a projection matrix.
Questions & Answers
QUESTION:
Apply the Spectral Theorem to establish that any symmetric matrixAsatisfyingA2 = A is in fact a projection matrix.
ANSWER:Step 1 of 2
It is given that is a symmetric matrix satisfying,
.
The Spectral theorem is stated as,
Let be a symmetric matrix. Then the Eigenvalues of are real and there is an orthogonal matrix such that,
is diagonal.
To prove that is the projection matrix.