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Course content |
Vectors in Rn, notion of linear independence and dependence, linear span of a set of vectors, vector subspaces of Rn, basis of a vector subspace. Systems of linear equations, matrices and Gauss elimination, row space, null space, and column space, rank of a matrix. Determinants and rank of a matrix in terms of determinants. Abstract vector spaces, linear transformations, matrix of a linear transformation, change of basis and similarity, rank-nullity theorem. Inner product spaces, Gram-Schmidt process, orthonormal bases, projections and least squares approximation. Eigenvalues and eigenvectors, characteristic polynomials, eigenvalues of special matrices (orthogonal, unitary, hermitian, symmetric, skew-symmetric, normal). Algebraic and geometric multiplicity, diagonalization by similarity transformations, spectral theorem for real symmetric matrices, application to quadratic forms.
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Texts/References |
- H. Anton, Elementary linear algebra with applications (8th Edition), John Wiley (1995).
- G. Strang, Linear algebra and its applications (4th Edition), Thomson (2006)
- S. Kumaresan, Linear algebra - A Geometric approach, Prentice Hall of India (2000)
- E. Kreyszig, Advanced engineering mathematics (10th Edition), John Wiley (1999)
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