Shortcuts | Syllabus LA | Notes LA | Syllabus HLA1 | Notes HLA1 | Syllabus HLA2 | Notes HLA2
This is a series of undergraduate-level courses at NYU Shanghai.
Course information
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Instructor: Shengkui Ye & Eric Endo
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Semester: Fall 2022, Spring 2022, Fall 2023
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Outline: Vector space, linear maps and matrix algebra, isomorphisms, subspaces; Row reduction, reduced form, general solution, linear dependence, dimension, change ofbasis Kernel, range, row space, rank theorem, rank-nullity theorem; Determinant, motivation as signed volume, construction, properties, existence and uniqueness; Eigenvalues, eigenvectors, characteristic polynomial, complex upper triangular representation; Dot product, symmetric matrices, spectral theorem; Dot product, orthogonal basis, projections, Gram-Schmidt orthogonalization process, Least square solutions; Inner product on real vectors spaces and complex vector spaces, isometries and unitary matrices; Upper triangular (Schur) representation of an operator, Spectral theorem for self-adjoint and normal operators, Polar and singular value decompositions, Structure of orthogonal matrices; Bilinear and quadratic forms， Diagonalization of quadratic forms， Silvesters Law of Inertia，Positive definite forms. Minimax characterization of eigenvalues and the Silvester’s criterion of positivity，Positive definite forms and inner products; minimal polynomials, Jordan form, computing a Jordan basis
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Textbook: Linear Algebra Done Wrong [2017] (Sergei Treil); Linear Algebra Done Right [2015] (Sheldon Axler); Linear Algebra and Its Applications [5th Edition] (David C. Lay)
Gradebook
Overall grade: A (8.00/8.00)