Difference between revisions of "MAT5283"
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Introduction to the theory of finite-dimensional vector spaces. | Introduction to the theory of finite-dimensional vector spaces. | ||
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'''Catalog entry''' | '''Catalog entry''' | ||
| − | ''Prerequisite'': Algebra | + | ''Prerequisite'': Prerequisite: Math 2233 Linear Algebra, Math 2243 Applied Linear Algebra or instructor approval. , or instructor consent. |
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| − | + | ''Contents'': | |
| − | + | (1) Algebraic Structures: rings, matrices, polynomials, fields and finite fields (2) Vector | |
| − | + | spaces: subspaces, linear independence, basis, dimension (3) Linear transformations, isomor- | |
| − | + | phisms, Rank-Nullity Theorem, Product and Quotient Spaces (3) Matrices and Linear Transfor- | |
| − | + | mations: Matrix representation, change of basis, equivalence of matrices, similarity (4) Eigen- | |
| − | + | values and Eigenvectors: The Cayley-Hamilton Theorem, Diagonalization and Jordan Canoni- | |
| − | + | cal forms (4) Real and Complex Inner Product Spaces: Norm, distances, Cauchy-Schwartz in- | |
| − | + | equality, Gram-Schmidt Orthogonalization process, The Projection Theorem, Riez Representa- | |
| − | + | tion Theorem (5) Orthogonality over finite fields (6) Multilinear algebra : Bilinear Forms and | |
| − | + | Functionals, Tensor product of vector spaces and Matrices. | |
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Latest revision as of 19:48, 24 March 2026
Introduction to the theory of finite-dimensional vector spaces.
Catalog entry
Prerequisite: Prerequisite: Math 2233 Linear Algebra, Math 2243 Applied Linear Algebra or instructor approval. , or instructor consent.
Contents: (1) Algebraic Structures: rings, matrices, polynomials, fields and finite fields (2) Vector spaces: subspaces, linear independence, basis, dimension (3) Linear transformations, isomor- phisms, Rank-Nullity Theorem, Product and Quotient Spaces (3) Matrices and Linear Transfor- mations: Matrix representation, change of basis, equivalence of matrices, similarity (4) Eigen- values and Eigenvectors: The Cayley-Hamilton Theorem, Diagonalization and Jordan Canoni- cal forms (4) Real and Complex Inner Product Spaces: Norm, distances, Cauchy-Schwartz in- equality, Gram-Schmidt Orthogonalization process, The Projection Theorem, Riez Representa- tion Theorem (5) Orthogonality over finite fields (6) Multilinear algebra : Bilinear Forms and Functionals, Tensor product of vector spaces and Matrices.
