Assuming no prior knowledge of linear algebra, this self-contained text offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book covers important topics in linear algebra that are useful for statisticians, including the concept of rank, the fundamental theorem of linear algebra, projectors, and quadratic forms. It also provides an extensive collection of exercises on theoretical concepts and numerical computations.

Sudipto Banerjee, Anindya Roy

Matrices, Vectors, and Their Operations. Systems of Linear Equations. More on Linear Equations. Euclidean Spaces. The Rank of a Matrix. Complementary Subspaces. Orthogonality, Orthogonal Subspaces, and Projections. More on Orthogonality. Revisiting Linear Equations. Determinants. Eigenvalues and Eigenvectors. Quadratic Forms. The Kronecker Product and Related Operations. Linear Iterative Systems, Norms, and Convergence. Abstract Linear Algebra. References.