By the end of the course the student will learn
- definitions of eigenvalues, eigenvectors and their computations,
- diagonalizability, its uses and diagonalization process, simultaneous diagonalization,
- minimal and characteristic polynomials of linear operators/matrices, Cayley-Hamilton Theorem,
- definition of Jordan canonical form and rational canonical form,
- methods of finding Jordan canonical form of matrices,
- some applications about Jordan canonical forms,
- definition of inner product, norm and their basic properties,
- definition of orthogonal and orthonormal bases and their basic properties,
- definition and computation of orthogonal projection and orthogonalization,
- definition and basic properties of adjoints of linear operators on inner product spaces,
- definitions and basic properties of normal, orthogonal, unitary, self-adjoint linear operators/matrices.