Linear Algebra
A.R. Vasishtha
SYLLABUS- LINEAR ALGEBRA,
Linear Transformations: Linear transformations, rank and nullity, Linear operators, Algebra of linear transformations, Invertible linear transformations, isomorphism; Matrix of a linear transformation, Matrix of the sum and product of linear transformations, Change of basis, similarity of matrices.
Linear Functionals: Linear functional, Dual space and dual basis, Double dual space, Annihilators, hyperspace; Transpose of a linear transformation.
Eigen vectors and Eigen values: Eigen vectors and Eigen values of a matrix, product of characteristic roots of a matrix and basic results on characteristic roots, nature of the characteristic roots of Hermitian, skew-Hermitian, unitary and orthogonal matrices, characteristic equation of a matrix, Cayley-Hamilton theorem and its use in finding inverse of a matrix.
Bilinear forms: Bilinear forms, symmetric and skew-symmetric bilinear forms, quadratic form associated with a bilinear form.
Linear Transformations: Linear transformations, rank and nullity, Linear operators, Algebra of linear transformations, Invertible linear transformations, isomorphism; Matrix of a linear transformation, Matrix of the sum and product of linear transformations, Change of basis, similarity of matrices.
Linear Functionals: Linear functional, Dual space and dual basis, Double dual space, Annihilators, hyperspace; Transpose of a linear transformation.
Eigen vectors and Eigen values: Eigen vectors and Eigen values of a matrix, product of characteristic roots of a matrix and basic results on characteristic roots, nature of the characteristic roots of Hermitian, skew-Hermitian, unitary and orthogonal matrices, characteristic equation of a matrix, Cayley-Hamilton theorem and its use in finding inverse of a matrix.
Bilinear forms: Bilinear forms, symmetric and skew-symmetric bilinear forms, quadratic form associated with a bilinear form.
年:
2021
语言:
english
页:
196
ISBN:
B095Y9BGCB
文件:
PDF, 2.01 MB
IPFS:
,
english, 2021
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