Linear Algebra

Code: MA1410H | L-T-P-C: 3-1-0-4

Systems of linear equations, matrices, Gaussian elimination, echelon form, column space, null space, rank of a matrix, inverse and determinant; Vector spaces over the field of real and complex numbers, subspaces, spanning set, linear independence, basis and dimension; Linear transformations, rank-nullity theorem, matrix of a linear transformation, change of basis and similarity; Eigenvalues and eigenvectors, algebraic and geometric multiplicity, diagonalization by similarity; Inner-product spaces, Gram-Schmidt process, orthonormal basis; Orthogonal, Hermitian and symmetric matrices, spectral theorem for real symmetric matrices.

Texts:

• D. Poole, Linear Algebra: A Modern Introduction, Cengage Learning India Private Limited, Fourth Edition, 2015.

References:

• G. Strang, Linear Algebra and Its Applications, Cengage Learning, Fourth Edition, 2006
• . Gilbert and L. Gilbert, Linear Algebra and Matrix Theory, Academic Press, 1995.
• K. Hoffman and R. Kunze, Linear Algebra, Pearson India, Second Edition, 2015.