Eigenvalues and Eigenvectors of Linear Operators (matrices). Characteristic and Minimal Polynomials. Diagonalization of Matrices. Triangular Form of a Linear Operator. Cayley-Hamilton Theorem. Direct-Sum Decomposition. Invariant Subspaces. The Primary Decomposition Theorem. Jordan Normal Form. Inner Product Spaces. Linear Functionals. Adjoint of a Matrix. Self-Adjoint, Unitary and Normal Operators. Orthogonal Projections. Spectral Theorem for Self-Adjoint, Unitary and Normal Operators. Bilinear and Quadratic Forms.

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