LINEAR ALGEBRA Second Edition KENNETH HOFFMAN , RAY KUNZE

LINEAR ALGEBRA Second Edition KENNETH HOFFMAN , RAY KUNZE

    In this book, topics are divided in ten chapters as per following :

     Chapter 1 deals with systems of linear equations and their solution by means of elementary row operations on matrices. 

   Chapter 2 deals with vector spaces, subspaces, bases, and dimension. 

   Chapter 3 treats linear transformations, their algebra, their representation by matrices, as well as isomorphism, linear functionals, and dual spaces.

   Chapter 4 defines the algebra of polynomials over a field, the ideals in that algebra, and the prime factorization of a polynomial. It also deals with roots, Taylor’s formula, and the Lagrange inter- polation formula. 

   Chapter 5 develops determinants of square matrices, the deter- minant being viewed as an alternating n-linear function of the rows of a matrix, and then proceeds to multilinear functions on modules as well as the Grassman ring. 

   Chapters 6 and 7 contain a discussion of the concepts which are basic to the analysis of a single linear transformation on a finite-dimensional vector space; the analysis of charac- teristic (eigen) values, triangulable and diagonalizable transformations; the con- cepts of the diagonalizable and nilpotent parts of a more general transformation, and the rational and Jordan canonical forms. 

   Chapter 7 includes a discussion of matrices over a polynomial domain, the computation of invariant factors and elementary divisors of a matrix, and the development of the Smith canonical form. The chapter ends with a dis- cussion of semi-simple operators, to round out the analysis of a single operator.

   Chapter 8 treats finite-dimensional inner product spaces in some detail. 

   Chapter 9 introduces sesqui-linear forms, relates them to positive and self-adjoint operators on an inner product space, moves on to the spectral theory of normal operators and then to more sophisticated results concerning normal operators on real or complex inner product spaces. 

   Chapter 10 discusses bilinear forms, emphasizing canonical forms for symmetric and skew-symmetric forms, as well as groups preserving non-degenerate forms, especially the orthogonal, unitary, pseudo-orthogonal and Lorentz groups. 

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