Apply the Spectral Theorem to establish that any symmetric matrixAsatisfyingA2 = A is in

Chapter 6, Problem 10

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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.

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