Linear Mathematics
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On the Teaching of Linear Algebra
Author: J.-L. Dorier
language: en
Publisher: Springer Science & Business Media
Release Date: 2000-09-30
This book presents the state-of-the-art research on the teaching and learning of linear algebra in the first year of university, in an international perspective. It provides university teachers in charge of linear algebra courses with a wide range of information from works including theoretical and experimental issues.
Linear Algebra
Author: H. E. Rose
language: en
Publisher: Springer Science & Business Media
Release Date: 2002
Linear algebra is one of the most important branches of mathematics - important because of its many applications to other areas of mathematics, and important because it contains a wealth of ideas and results which are basic to pure mathematics. This book gives an introduction to linear algebra, and develops and proves its fundamental properties and theorems taking a pure mathematical approach - linear algebra contains some fine pure mathematics. Main topics: - vector spaces and algebras, dimension, linear maps, direct sums, and (briefly) exact sequences - matrices and their connections with linear maps, determinants (properties proved using some elementary group theory), and linear equations - Cayley-Hamilton and Jordan theorems leading to the spectrum of a linear map - this provides a geometric-type description of these maps - Hermitian and inner product spaces introducing some metric properties (distance, perpendicularity etc.) into the theory, also unitary and orthogonal maps and matrices - applications to finite fields, mathematical coding theory, finite matrix groups, the geometry of quadratic forms, quaternions and Cayley numbers, and some basic group representation theory A large number of examples, exercises and problems are provided. Answers and/or sketch solutions to all of the problems are given in an appendix. Some of these are theoretical and some numerical, both types are important. No particular computer algebra package is discussed but a number of the exercises are intended to be solved using one of these packages chosen by the reader.The approach is pure-mathematical, and the intended readership is undergraduate mathematicians, also anyone who requires a more than basic understanding of the subject. This book will be most useful for a "second course" in linear algebra, that is for students that have seen some elementary matrix algebra. But as all terms are defined from scratch, the book can be used for a "first course" for more advanced students.
Linear Algebra
Author: Georgi? Evgen?evich Shilov
language: en
Publisher: Courier Corporation
Release Date: 1977-06-01
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.