# Krishna’s TB Vector Spaces & Matrices, Edition

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.

**Authors:** A.R Vasishtha

**Date:** 2021

**Upload Date:** 9/30/2021 9:53:25 AM

**Format:** pdf

**Pages:** 1

**OCR:**

**Quality:**

**Language:** English

**ISBN / ASIN:** B092TGTL77

**ISBN13:**

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