Krishna's TB Linear Algebra|Edition-1B|Pages-296|Code-1037

by A.R. Vasishtha

SYLLABUS- LINEAR ALGEBRA, Linear Algebra Vector spaces and their elementary properties, Subspaces, Linear dependence and independence, Basis and dimension, Direct sum, Quotient space. Linear transformations and their algebra, Range and null space, Rank and nullity, Matrix representation of linear transformations, Change of basis. Linear functionals, Dual space, Bi-dual space, Natural isomorphism, Annihil- ators, Bilinear and quadratic forms, Inner product spaces, Cauchy-Schwarz's inequality, Bessel's inequality and orthogonality. Matrices Symmetric and skew-symmetric matrices, Hermitian and skew-Hermitian matrices, Orthogonal and unitary matrices, Triangular and diagonal matrices, Rank of a matrix, Elementary transformations, Echelon and normal forms, Inverse of a matrix by elementary transformations. Characteristic equation, Eigen values and eigen vectors of a matrix, Cayley- Hamilton's theorem and its use in finding inverse of a matrix, Application of matrices to solve a system of linear (both homogeneous and non-homogeneous) equations, Consistency and general solution, Diagonalization of square matrices

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Published April 4, 2021