MA 106: Linear Algebra

Course Code MA 106
Course Name Linear Algebra
Lecture 3
Tutorial 1
Practical 0
Credit 4*
Reference 1. H. Anton, Elementary linear algebra with applications (8th Edition), John Wiley (1995).2. G. Strang, Linear algebra and its applications (4th Edition), Thom- son(2006).3. S. Kumaresan, Linear algebra - A Geometric approach, Prentice Hall of India (2000).4. E. Kreyszig, Advanced engineering mathematics (8th Edition), John Wiley (1999).
Description Vectors in Rn , notion of linear independence and dependence, linearspan of a set of vectors, vector subspaces of Rn , basis of a vectorsubspace.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 trans-formation, change of basis and similarity, rank-nullity theorem.Inner pro duct spaces, Gram-Schmidt pro cess, orthonormal bases, pro-jections and least squares approximation.Eigenvalues and eigenvectors, characteristic polynomials, eigenvaluesof special matrices ( orthogonal, unitary, hermitian, symmetric, skew-symmetric, normal). algebraic and geometric multiplicity, diagonaliza-tion by similarity transformations, spectral theorem for real symmetricmatrices, application to quadratic forms.