Covers vectors, matrix algebra, linear-algebra, linear-equations, determinants, mappings, canonical forms, linear functions, and quadratic forms Helping you master linear algebra, this guide also helps you cut study time and hone problem-solving skills. It includes: 3000 solved problems with complete solutions; an index to help you locate the types of problems you want to solve; problems like those you'll find on your exams; and techniques for choosing the correct approach to problems. Vectors in R and C.Matrix Algebra.Systems of Linear Equations.Square Matrices.Determinants.Algebraic Structures.Vector Spaces and Subspaces.Linear Dependence, Basis, Dimension.Mappings.Linear Mappings.Spaces of Linear Mappings.Matrices and Linear Mappings.Change of Basis, Similarity.Inner Product Spaces, Orthogonality.Polynomials Over A Field.Eigenvalues and Eigenvectors.Diagonalization.Canonical Forms.Linear Functional and the Dual Space.Bilinear, Quadratic, and Hermitian Forms.Linear Operators on Inner Product Spaces.Applications to Geometry and Calculus.