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Math / Linear Algebra: A Geometric Approach 2 / Chapter 6.4 / Problem 11

Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams

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a. Suppose A is a symmetric n n matrix satisfying A4 = I . Use the Spectral Theorem to

Chapter 6, Problem 11

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QUESTION:

a. Suppose is a symmetric matrix satisfying, . Use Spectral theorem to give a complete description of .

b. What happens for a symmetric matrix satisfying for some integer ?

Questions & Answers

QUESTION:

a. Suppose is a symmetric matrix satisfying, . Use Spectral theorem to give a complete description of .

b. What happens for a symmetric matrix satisfying for some integer ?

ANSWER:

Step 1 of 3

It is given that is a symmetric matrix satisfying the condition,

.

The Spectral theorem is stated as,

Let be a symmetric matrix. Then the Eigen values of are real and there is an orthonormal basis for consisting of Eigen vectors of, . That is, there is an orthogonal matrix such that,

is diagonal.

To find

a. The description of .

b. What happens for a symmetric matrix, satisfying for some integer .

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