Vector Spaces & Matrices
Vector Spaces & Matrices by A.R Vasishtha
English | 2021 | ISBN: N/A | ASIN: B092TGTL77 | 2021 pages | PDF | 2.28 Mb
English | 2021 | ISBN: N/A | ASIN: B092TGTL77 | 2021 pages | PDF | 2.28 Mb
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.
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