(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A linear operator given (a matrix). That could be an orthogonal protection (that goes through the origin) or a symmetry with respect to a plane (that goes through the origin).

1-Get the eigenvalues of linear operator

2-Get the eigenspace associated with each eigenvalue.

3-Based on the previous calculations determine if the Operator is a symmetry or an orthogonal protection.

4-Describe an ortogonal base of the given plane, and complete it with a base of R^2

The matrix with respect to the calculated base must have the form of the orthogonal projection or of the symmetric matrix

100 or 100

010 010

00-1 000

2. Relevant equations

3. The attempt at a solution

I got the eigenvalues 1 and 0 therefore I'm assuming the operator is an orthogonal projection.

I got the eigenvectors

How can I start to do 4?

Im thinking about using gram schidt to get 3 ortogonal vectors and then to use them as a base .

Thanks a lot for any help, I appreciate it.

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# Homework Help: Problem about Eigenvalues

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