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Chapter 7: Q35E (page 383)

If v is an eigenvector of A, then v must be an eigenvector of ATas well.

Short Answer

Expert verified

If v is an eigenvector of A, then v must be an eigenvector of ATas well.

Step by step solution

01

Define eigenvalue:

Eigenvalues are a set of specialized scales associated with a system of linear equations. The corresponding eigenvalue, often denoted by 位.

02

Explanation for eigenvalues:

For example,

A=0101

Clearly,

v=11

is an eigenvector of A, with the corresponding eigenvalues位=1. However,

ATv=001111=01,

which is not collinear with v. So, is not an eigenvalue of AT.

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