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Vectors in R and C, Spatial Vectors. Algebra of Matrices. Systems of Linear Equations. Vector Spaces. Linear Mappings. Linear Mappings and Matrices. Inner Product Spaces, Orthogonality. Determinants. Diagolnalization: Eigenvalues and Eigenvectors. Canonical Forms. Linear Functionals and the Dual Space. Bilinear, Quadratic, and Hermitian Forms. Linear Operators on Inner Product Spaces. Multilinear Products. List of Symbols.