Eigensystems - canonical forms

Let A be a normal matrix. Select all the statements that apply.

• A is always a square matrix.

• A and A^* commute.

• A^*A = I

• A^*A = A

For a normal matrix A, which of the following is correct?

• The eigenvalues of A are all real.

• A is unitarily similar to a diagonal matrix.

• A is defective.

A matrix A is diagonalizable if and only if ...

• A is normal.

• A has a full set of linearly independent eigenvectors.

• A has disctinct eigenvalues.

• its eigenvectors are mutually orthogonal.

• Yes

• No

• Yes

• No

Let A be an nxn Jordan block with eigenvalue μ. What is the geometric multiplicity of μ?

• 1

• n

• 0

• n-1