EAN: 9783319637921

COMPACT TEXTBOOKS IN MATHEMATICS LINEAR ALGEB...

This self-contained  clearly written textbook on linear algebra is easily accessible for
students. It begins with the simple linear equation and generalizes several notions from this
equation for the system of linear equations and introduces the main ideas using matrices. It
then offers a detailed chapter on determinants and introduces the main ideas with detailed
proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and
discusses various major inequalities and identities. These ideas offer a solid basis for
understanding general Hilbert spaces in functional analysis. The following two chapters address
general vector spaces  including some rigorous proofs to all the main results  and linear
transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6
introduces the idea of matrices using linear transformation  which is easier to understand than
the usual theory of matrices approach. The final two chapters are more advanced  introducing
the necessary concepts of eigenvalues and eigenvectors  as well as the theory of symmetric and
orthogonal matrices. Each idea presented is followed by examples. The book includes a set of
exercises at the end of each chapter  which have been carefully chosen to illustrate the main
ideas. Some of them were taken (with some modifications) from recently published papers  and
appear in a textbook for the first time. Detailed solutions are provided for every exercise 
and these refer to the main theorems in the text when necessary  so students can see the tools
used in the solution.

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