True False. If A is nonsingular, then any eigenvalues are nonzero.

True False. If A is similar to B then they have the same eigenvalues.

True False. The eigenvalues of a Hermitian matrix are distinct.

True False. If Ax = 2x , Ay = 3y and Az = 4z , all nonzero, then {x, y, z} is L I.

True False. If A is real and A^TA =AA^T then A is normal.

True False. If A is similar to a diagonal matrix D, then A has n orthogonal eigenvectors.

True False. Every real symmetric matrix is diagonalizable.

True False. The columns of a diagonalizing matrix X are eigenvectors of A.

True False. The columns of any unitary matrix U are orthonormal, and U^HU = I.

True False. Every nondefective nxn matrix A has n distinct eigenvalues.

Written by S.Hudson