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Suppose A = uvT is a column times a row (a rank-1 matrix). (a) By multiplying A times u

Chapter 5, Problem 5.2.8

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QUESTION:

Suppose A = uvT is a column times a row (a rank-1 matrix). (a) By multiplying A times u, show that u is an eigenvector. What is ? (b) What are the other eigenvalues of A (and why)? (c) Compute trace(A) from the sum on the diagonal and the sum of s.

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QUESTION:

Suppose A = uvT is a column times a row (a rank-1 matrix). (a) By multiplying A times u, show that u is an eigenvector. What is ? (b) What are the other eigenvalues of A (and why)? (c) Compute trace(A) from the sum on the diagonal and the sum of s.

ANSWER:

Step 1 of 4

(a)

The objective is to determine that  is an eigenvector of  by the associative property of the vector multiplication.

                                                                     

 

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