Linear Algebra
Linear Algebra by A.R Vasishtha
English | 2021 | ISBN: N/A | ASIN: B095S9RQ4J | 461 pages | PDF | 4.24 Mb
English | 2021 | ISBN: N/A | ASIN: B095S9RQ4J | 461 pages | PDF | 4.24 Mb
SYLLABUS- LINEAR ALGEBRA,
Unit-1:Vector spaces and their elementary properties, subspaces, linear dependence and independence, basis and dimension, direct sum, quotient space.
Unit-2:Linear transformations and their algebra, range and null space, rank and nullity, matrix representation of linear transformations, changes of basis.
Unit-3:Linear functionals, dual space. Bi-dual space, natural isomorphism. Annihilators, bilinear and quadratic forms, inner product spaces, cauchy-schwarz's inequality. Bessel's inequality an orthogonality.
Unit-4: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.
Unit-5: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 with distinct eigen values.
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