Advanced Linear Algebra (Textbooks in Mathematics) by Nicholas Loehr

By Nicholas Loehr

Designed for complex undergraduate and starting graduate scholars in linear or summary algebra, Advanced Linear Algebra covers theoretical features of the topic, besides examples, computations, and proofs. It explores a number of complicated subject matters in linear algebra that spotlight the wealthy interconnections of the topic to geometry, algebra, research, combinatorics, numerical computation, and lots of different parts of arithmetic.

The book’s 20 chapters are grouped into six major components: algebraic constructions, matrices, dependent matrices, geometric facets of linear algebra, modules, and multilinear algebra. the extent of abstraction steadily raises as scholars continue during the textual content, relocating from matrices to vector areas to modules.

Each bankruptcy comprises a mathematical vignette dedicated to the advance of 1 particular subject. a few chapters examine introductory fabric from a cosmopolitan or summary perspective whereas others offer trouble-free expositions of extra theoretical suggestions. numerous chapters supply strange views or novel remedies of normal effects. not like related complex mathematical texts, this one minimizes the dependence of every bankruptcy on fabric present in earlier chapters in order that scholars might instantly flip to the suitable bankruptcy with out first wading via pages of prior fabric to entry the required algebraic historical past and theorems.

Chapter summaries include a established record of the important definitions and effects. End-of-chapter workouts reduction scholars in digesting the cloth. scholars are inspired to take advantage of a working laptop or computer algebra method to aid resolve computationally in depth exercises.

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