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Indian Institute of Science Education and Research Bhopal
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 Rn and Cn, matrix equation Ax = b, row-reduced echelon form, row space, column space, and rank of a matrix. Determinants. Systems of linear equations
Vector space Rn, 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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