5.1 FIELDS AND VECTOR SPACES5.2 LINEAR COMBINATIONS, GENERATORS, AND BASES5.3 COMPONENTS5.4 LINEAR TRANSFORMATIONS5.5 MATRIX REPRESENTATION OF TRANSFORMATIONS5.6 ALGEBRA OF TRANSFORMATIONS5.7 CHANGE OF BASIS5.8 INVARIANTS UNDER SIMILARITY TRANSFORMATIONS5.9 EIGENVALUES AND EIGENVECTORS5.10 MOMENT OF INERTIA TENSOR5.11 INNER PRODUCT SPACES5.12 THE INNER PRODUCT5.13 ORTHOGONALITY AND COMPLETENESS5.14 GRAM–SCHMIDT ORTHOGONALIZATION5.15 EIGENVALUE PROBLEM FOR REAL SYMMETRIC MATRICES5.16 PRESENCE OF DEGENERATE EIGENVALUES5.17 QUADRATIC FORMS5.18 HERMITIAN MATRICES5.19 MATRIX REPRESENTATION OF HERMITIAN OPERATORS5.20 FUNCTIONS OF MATRICES5.21 FUNCTION SPACE AND HILBERT SPACE5.22 DIRAC'S BRA AND KET VECTORSREFERENCESPROBLEMS