Beginning with the basic concepts of vector spaces such as linear independence, basis and dimension, quotient space, linear transformation and duality with an exposition of the theory of linear operators on a finite dimensional vector space, this book includes the concepts of eigenvalues and eigenvectors, diagonalization, triangulation and Jordan and rational canonical forms. Inner product spaces which cover finite dimensional spectral theory, and an elementary theory of bilinear forms are also discussed.
V. Sahai.: Department of Mathematics and Astronomy Lucknow University, Lucknow, India V. Bist.: Department of Mathematics, Punjab University, Chandigarh, India
Preface / Preliminaries: Matrices / Elementary operations on matrices / Determinants / Systems of linear equations / Polynomials / Vector Spaces: Definition and examples / Subspaces / basis and dimension / Linear transformation / Quotient spaces / Direct sum / The matrix of a linear transformation / Duality / Canonical Forms: Eigenvalues and eigenvectors / The minimal polynomial / Diagonalizable and triangulable operators / The Jordan form / The rational form / Inner Product Spaces: Inner products / Orthogonality / The adjoint and normal operators / Polar and singular value decompositions / Bilinear Forms: Definition and examples / The matrix of a bilinear form / Orthogonality / Classification of bilinear forms / Bibliography / Index