EExxx: Linear Algebra and its Applications - SyllabusDepartment of Electrical Engineering, Indian Institute of Technology Dharwad
SyllabusFollowing is the detailed course content. Please note that these topics just form a guideline and may not be covered completely. They may be modified dynamically. Systems of Linear Equations: Matrix-vector representation, elementary row operations, row-reduced echelon form, solving a system of linear equations. Vector Spaces: Fields, vector-space, subspaces, sums and intersections of subspaces, span, linear independence, bases, dimensions, basis extension, coordinates, quotienting. Linear Maps: Definition, nullkernel space, rangeimage spaces, matrix representation of linear maps, ranks, rank-nullity theorem, algebra of linear maps, linear functionals, the double dual. Polynomials: Rings, ideals, PIDs, prime factorization, quotient ring. Eigenvalues and eigenvectors: Eigenvalues, eigenvectors, polynomials of a linear map, annihilating polynomial, minimal polynomial, Caley-Hamilton theorem, invariant subspaces, direct sum decomposition, cyclic subspaces, Jordan canonical form. Inner Product Spaces: Inner products, orthogonality, Gram-Schimdt orthogonalization, orthogonal complement, spectral theory of operators on an inner product space. Projections: Orthogonal projections, product of projections, projection theorem for Hilbert spaces. Numerical Linear Algebra: Iterative methods of solving a system of linear equations, norms, SVD. Applications:
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