Linear Algebra Reading Group

This reading group covers the fourth edition of "Linear Algebra" by Friedberg, Insel, and Spence. The sessions follow the textbook's progression through seven chapters, moving from foundational theory to advanced canonical forms. The group starts with Vector Spaces, establishing definitions for subspaces, linear independence, bases, and dimension. We then transition to Linear Transformations and Matrices, examining null spaces, ranges, matrix representations, and invertibility. This stage also includes the study of dual spaces. The curriculum continues with Elementary Matrix Operations and Systems of Linear Equations, focusing on rank and matrix inverses. This leads into an analysis of Determinants, covering their properties and characterizations. In the latter half, the group focuses on Diagonalization, specifically eigenvalues, eigenvectors, and the Cayley-Hamilton Theorem. This is followed by a detailed study of Inner Product Spaces, including the Gram-Schmidt process, normal and self-adjoint operators, the Spectral Theorem, and Singular Value Decomposition (SVD). Finally, we cover Canonical Forms, including the Jordan Canonical Form, minimal polynomials, and the Rational Canonical Form. The group will engage with both theoretical proofs and computational applications as presented in the textbook's exercises.