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.