Linear Algebra

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Description:

Syllabus :

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.

Text Books :

1. D. Poole (2015). Linear Algebra: A Modern Introduction (4th ed.). Cengage Learning India Private Limited

Reference Books :

1. G. Strang (2006). Linear Algebra and Its Applications. Cengage Learning
2. J. Gilbert & L. Gilbert (1995). Linear Algebra and Matrix Theory. Academic Press
3. K. Hoffman & R. Kunze (2015). Linear Algebra (2nd ed.). Pearson India