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MAT 1001: Linear Algebra

Syllabus: Real vector spaces, subspaces, spanning sets, basis sets, dimension of a vector space.  Solution of a system of linear equations. Row space and column space of a matrix, rank of a matrix, elementary row and column operations of a matrix. Inversion of square matrices, rank factorization of a matrix. Properties of determinants. Linear transformations, range and null space of a linear transformation, rank-nullity theorem. Matrix representation of a linear transformation. Inner product spaces, normed linear spaces, examples of different normed linear spaces, orthonormal basis sets. Eigenvalues, eigenvectors, characteristic polynomials. Spectral theorem for real symmetric matrices. Singular value decompositions.

References:

  1. A. R. Rao and P. Bhimsankaram: Linear algebra, Hindustan book agency, 2000.
  2. S. H. Friedberg, A. J. Insel and L. E. Spence: Linear algebra, Pearson, 2015.
  3. D. C Lay: Linear algebra and its applications, Pearson, 2014.

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Study at Ashoka