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.