Difference between revisions of "MAT5283"
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Jose.iovino (talk | contribs) (Created page with " A study of linear algebraic structures that may include linear transformations, inner product spaces, eigenvalues, Cayley-Hamilton theorem, similarity, the Jordan canonical f...") |
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| − | + | (1) Vector spaces: Abstract vector spaces, subspaces, bases, dimension, sums and direct sums. (2) Linear transformations: Rank and nullity, isomorphisms, bases, change of basis, canonical forms. (3) Inner product spaces: Norm, angles, orthogonal and orthonormal sets, orthogonal complement, best approximation and least squares, Riesz Representation Theorem. (4) Determinants: Axiomatic characterization of determinants, multilinear functions, existence and uniqueness of determinants. (5) Eigenvalues and eigenvectors: Characteristic polynomials, eigenspaces. (6) Block diagonal representation: Diagonalizability, triangularizability, block representation, Jordan normal form. (6) The Spectral Theorem. | |
Revision as of 14:47, 9 March 2023
(1) Vector spaces: Abstract vector spaces, subspaces, bases, dimension, sums and direct sums. (2) Linear transformations: Rank and nullity, isomorphisms, bases, change of basis, canonical forms. (3) Inner product spaces: Norm, angles, orthogonal and orthonormal sets, orthogonal complement, best approximation and least squares, Riesz Representation Theorem. (4) Determinants: Axiomatic characterization of determinants, multilinear functions, existence and uniqueness of determinants. (5) Eigenvalues and eigenvectors: Characteristic polynomials, eigenspaces. (6) Block diagonal representation: Diagonalizability, triangularizability, block representation, Jordan normal form. (6) The Spectral Theorem.
