Systems of linear equations, Matrices, Elementary row operations, Row-reduced echelon matrices. Vector spaces, Subspaces, Bases and dimension, Ordered bases and coordinates.

Linear transformations, Rank-nullity theorem, Algebra of linear transformations, Isomorphism, Matrix representation, Linear functionals, Annihilator, Double dual, Transpose of a linear transformation.

Characteristic values and characteristic vectors of linear transformations, Diagonalizability, Minimal polynomial of a linear transformation, Cayley-Hamilton theorem, Invariant subspaces, Direct-sum decompositions, Invariant direct sums, The primary decomposition theorem, Cyclic subspaces and annihilators, Cyclic decomposition, Rational, Jordan forms.

K.Hoffman and R. Kunze, Linear Algebra, 2nd Edition, Prentice- Hall of India, 2005.

M. Artin, Algebra, Prentice-Hall of India, 2005.

S. Axler, Linear Algebra Done Right, 2nd Edition, John-Wiley, 1999.

S. Lang, Linear Algebra, Springer UTM, 1997.

S. Kumaresan, Linear Algebra: A Geometric Approach, Prentice-Hall of India, 2004.

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