**MTH ****102: Linear Algebra**** ****(3)**

*Learning Objectives*:

This is the second core course in calculus designed for second year BS-MS students. The course deals with the multivariable calculus of vectors in dimension 2 and higher. The course concludes with an introduction to first order ODEs, and their solutions.

*Course Contents*:

Review of complex numbers

Matrices, matrix operations, special matrices (diagonal, triangular, symmetric, skew-symmetric, orthogonal, hermitian, skew hermitian, unitary, normal), vectors in** R ^{n}** and

**C**, matrix equation

^{n}**Ax = b**, row-reduced echelon form, row space, column space, and rank of a matrix. Determinants. Systems of linear equations

Vector space** R ^{n}**, linear independence and dependence, linear span, linear subspaces, bases and dimensions

Vector spaces, bases and dimensions, linear transformations, matrix of a linear transformation, rank-nullity theorem

Inner product spaces, orthonormal bases, Gram-Schmidt orthogonalization, projections

Eigenvalues and eigenvectors of a linear operator, characteristic polynomial, diagonalizability of a linear operator, eigenvalues of the special matrices stated above, spectral theorem for real symmetric matrices and its application to quadratic forms, positive definite matrices

*Suggested Books*:

- T. M. Apostol,
*Calculus,*Volume 2, 2nd edition, Wiley Eastern, 1980 - H. Anton,
*Elementary linear algebra and 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 - R. Rao and P. Bhimasankaram,
*Linear Algebra*, 2nd edition, Hindustan Book Agency, 2000 - M. Artin,
*Algebra*, Prentice-Hall of India, 1994 - R. Bapat,
*Linear Algebra and Linear Models,*HBA, 1999

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