A Second course in linear algebra/ Stephen Ramon Garcia and Roger A Horn

Preliminaries -- Vector spaces -- Bases and similarity -- Block matrices -- Inner product spaces -- Orthonormal vectors -- Unitary matrices -- Orthogonal complements and orthogonal projections -- Eigenvalues Eigenvectors and geometric multiplicity -- The Characteristic polynomial and algebraic multiplicity -- Unitary triangularization and block diagonalization -- Jordan canonical form -- Normal matrices and the spectral theorem -- Positive semidefinite matrices -- The Singular value and polar decompositions -- Singular values and the spectral norm -- Interlacing and inertia

Linear algebra is a fundamental tool in many fields, including mathematics and statistics, computer science, economics, and the physical and biological sciences. This undergraduate textbook offers a complete second course in linear algebra, tailored to help students transition from basic theory to advanced topics and applications. Concise chapters promote a focused progression through essential ideas, and contain many examples and illustrative graphics. In addition, each chapter contains a bullet list summarising important concepts, and the book includes over 600 exercises to aid the reader's understanding. Topics are derived and discussed in detail, including the singular value decomposition, the Jordan canonical form, the spectral theorem, the QR factorization, normal matrices, Hermitian matrices (of interest to physics students), and positive definite matrices