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Linear Algebra

Code: MA522 | L-T-P-C: 3-1-0-8

Systems of linear equations, vector spaces, bases and dimensions, change of bases and change of coordinates, sums and direct sums; Linear transformations, matrix representations of linear transformations, the rank and nullity theorem; Dual spaces, transposes of linear transformations; trace and determinant, eigenvalues and eigenvectors, invariant subspaces, generalized eigenvectors; Cyclic subspaces and annihilators, the minimal polynomial, the Jordan canonical form; Inner product spaces, orthonormal bases, Gram-Schmidt process; Adjoint operators, normal, unitary, and self-adjoint operators, Schur's theorem, spectral theorem for normal operators.


  1. S. Axler, Linear Algebra Done Right, 2nd Edn., UTM, Springer, Indian edition, 2010.
  2. K. Hoffman and R. Kunze, Linear Algebra, Prentice Hall of India, 1996.


  1. G. Schay, Introduction to Linear Algebra, Narosa, 1997.
  2. G. Strang, Linear Algebra and Its applications, Nelson Engineering, 4th Edn., 2007.