IIT MATH 532 - Math 532 – Linear Algebra (2 pages)

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Math 532 – Linear Algebra



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Math 532 – Linear Algebra

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2
School:
Illinois Institute of Technology
Course:
Math 532 - Linear Algebra

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Math 532 Linear Algebra Course Description from Bulletin Matrix algebra vector spaces norms inner products and orthogonality determinants linear transformations eigenvalues and eigenvectors Cayley Hamilton theorem matrix factorizations LU QR SVD 3 0 3 Enrollment Elective for AM and other majors Textbook s Carl D Meyer Matrix Analysis and Applied Linear Algebra SIAM 2000 ISBN 0 89871 454 0 Other required material none Prerequisites Undergraduate linear algebra as in MATH 332 or instructor s consent Objectives 1 Students will reinforce their understanding of matrix algebra in the context of the LU factorization 2 Students will understand the fundamental concepts of vector spaces 3 Students will understand vector and matrix norms along with the concept of an inner product space and learn how these concepts are applied in the context of orthogonal factorization algorithms such as Gram Schmidt QR and SVD 4 Students will understand eigenvalues and eigenvectors and how these concepts apply to matrix diagonalization and algorithms for computing eigenvalues and solving linear systems iteratively Lecture schedule 3 50 minutes or 2 75 minutes lectures per week Course Outline 1 Matrix Algebra a Inverse matrices and Sherman Morrison formula b Elementary matrices c LU factorization 2 Vector Spaces a Fundamental subspaces b Linear independence c Basis and dimension rank d Classical least squares e Linear transformations 3 Norms Inner Products and Orthogonality a Vector and matrix norms b Inner product spaces c Gram Schmidt orthogonalization QR factorization d Unitary and orthogonal matrices e Complementary subspaces f Orthogonal decomposition g Singular value decomposition Hours 4 10 16 h Orthogonal projections 4 Determinants 4 5 Eigenvalues and Eigenvectors 12 a Elementary properties b Diagonalization similarity transforms Cayley Hamilton theorem c Functions of diagonalizable matrices d Normal matrices e Positive definite matrices f Neumann series and iterative solvers g Krylov



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