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Description of  Krishna's TB Vector Spaces & Matrices, Edition- 2

ECTOR SPACES & MATRICES, Vector spaces: Vector space, sub spaces, Linear combinations, linear spans, Sums and direct sums. Bases and Dimensions: Linear dependence and independence, Bases and dimensions, Dimensions and subspaces, Coordinates and change of bases. Matrices: Idempotent, nilpotent, involutary, orthogonal and unitary matrices, singular and nonsingular matrices, negative integral powers of a nonsingular matrix Trace of a matrix. Rank of a matrix: Rank of a matrix, linear dependence of rows and columns of a matrix, row rank, column rank, equivalence of row rank and column rank, elementary transformations of a matrix and invariance of rank through elementary transformations, normal form of a matrix, elementary matrices, rank of the sum and product of two matrices, inverse of a non-singular matrix through elementary row transformations equivalence of matrices. Applications of Matrices: Solutions of a system of linear homogeneous equations, condition of consistency and nature of the general solution of a system of linear non- homogeneous equations, matrices of rotation and reflection.