The purpose of Math 33A is to provide mathematicians, engineers,
physical scientists, and economists with an introduction to the basic
ideas of linear algebra in n-dimensional Euclidean space. Abstract vector
spaces are not covered; they are treated in Math 115A.
Students in the course should have covered the following topics in
previous high school and college mathematics courses:
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solving linear systems of equations,
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matrices, matrix multiplication,
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two-by-two and three-by-three determinants,
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complex numbers,
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complex polynomials, the fundamental theorem of algebra.
This background material is reviewed in the course, though briefly.
The topics in linear algebra that are covered in Math 33A include:
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systems of linear equations, associated matrix equations,
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row reduction of a matrix,
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linear transformations,
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invertible matrices,
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subspaces, linear independence, bases, dimension,
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row space, column space, rank-nullity theorem,
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determinants,
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orthogonality, orthonormal bases,
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orthogonal matrices,
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Gram-Schmidt process, QR factorization,
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least-squares approximation, normal equations,
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eigenvalues, eigenvectors, similarity, diagonalization,
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applications to discrete dynamical systems,
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diagonalization of symmetric matrices,
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applications to quadratic forms, singular value decomposition.
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