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Linear Spaces and Operators, Matrices, Determinants and Permanents, Expansion Theorems, The Compound and Induced Matrices, The Kronecker Product, Unitary Spaces, The Characteristic Polynomial, Pencils Of Quadratic Forms and The Characterization of Eigenvalues By Extremal Problems, Field of Values, Inclusion Domains For Eigenvalues, Gershgorin's Theorem, Matrix and Vector Norms, Nonnegative Matrices, The Perron-frobenius Theorem, Doubly Stochastic Matrices, The Konig-frobenius Theorem and Birkhoff's Theorem, The Proof of The Van Der Waerden Conjecture For Permanents.

Faculty: Mathematics
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