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If A = QQ T is symmetric positive definite, then R = Q Q T is its symmetric positive

Chapter 6, Problem 6.2.7

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QUESTION:

If A = QQ T is symmetric positive definite, then R = Q Q T is its symmetric positive definite square root. Why does R have positive eigenvalues? Compute R and verify R 2 = A for A = " 10 6 6 10# and A = " 10 6 6 10#

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QUESTION:

If A = QQ T is symmetric positive definite, then R = Q Q T is its symmetric positive definite square root. Why does R have positive eigenvalues? Compute R and verify R 2 = A for A = " 10 6 6 10# and A = " 10 6 6 10#

ANSWER:

Step 1 of 7

Given that,

                                                             

Find the eigenvalues and eigenvectors of A as below.

                                         

The eigenvalues of A are 4 and 16.

 

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