Unformatted text preview: orthogonal projection of ! b on W = col(A). 7. Solve the eigenvalue problem A ! x = ! ! x for the eigenvalues and corresponding eigenvectors. 8. Each eigenvalue has an eigenspace. Find a basis for each eigenspace. 9. State the algebraic multiplicity and geometric multiplicity for each eigenvalue. 10. Let AP = PD for the symmetric matrix A and P. Show that P is an orthogonal matrix. 11. Find the eigenvalues of A by solving AP = PD for the diagonal matrix D; show that A = PDP T . 12. Compute the Wronskian and show that S is a linearly independent set of vectors....
View Full Document
- Summer '11
- Linear Algebra, Orthogonal matrix, Row echelon form, linearly independent set