June 23, 07

MA 106: Linear Algebra  (3-1-0-4)
Vectors in R^n, notion of linear independence and dependence, linear span of
a set of vectors, vector subspaces of R^n, basis of a vector space.
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 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 a
special matrices (orthonormal, unitary, hermitian, symmetric,
skew-symmetric, normal). Algebraic and geometric multiplicity,
diagonalization by similarity transformations, spectral theorem for real
symmetric matrices, application to quadratic forms.

Text/References
1. H. Anton, Elementary Linear Algebra with Applications, 8th ed., John
Wiley, 1995.
2. G. Strang, Linear Algebra and its Applications, 4th ed., Thomson, 2006.
3. S. Kumaresan, Linear Algebra-A Geometric Approach, Prentice Hall of
India, 2000.
4. E. Kreyszig, Advanced Engineering Mathematics, 8th ed., John Wiley, 1999.