Exam 8: Orthogonality

Determine , where .

The eigenvalues for the symmetric matrix A are given. Find matrices D and P of an orthogonal diagonalization of A.

If is an orthogonal basis for a subspace S of , and then is a diagonal matrix.

The singular value decomposition of a matrix A is unique.

The eigenvalues and corresponding eigenvectors for a symmetric matrix A are given. Find matrices D and P of an orthogonal diagonalization of A.

Find an orthogonal basis for the subspace .

If a system of equations has more variables than equations, then the system has infinitely many least squares solutions.

Determine if the given matrix is symmetric.

Every matrix A has a singular value decomposition.

If is a singular value decomposition for a matrix , then is an orthogonal diagonalizing matrix for .

Determine if the vectors form an orthogonal set.

If is a nonzero subspace of , and u belongs to , then .

If D is a diagonal matrix with diagonal entries , then the singular values of D are given by .

Find the least squares solution for the given system.

Express the given matrix as an outer product expansion , where and are the singular values of .

Determine if the given matrix is orthogonal.

Find the vector in the subspace S that is closest to y.

Find , where .

Find the least squares solution for the given system.

Find all least squares solutions for the given system.