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Ausfuhrlich werden in diesem Buch Aufgaben unterschiedlichen Schwierigkeitsgrades zu den Grundbegriffen der Mathematik, der Linearen Algebra und analytischen Geometrie sowie der Numerischen Algebra behandelt und deren Loesungen aufgezeigt. Ein Teil der Aufgaben zeigt Anwendungen und stellt Querverbindungen zu anderen mathematischen Gebieten her. Viele Hinweise zu den benoetigten mathematischen Grundlagen unterstutzen das selbstandige Bearbeiten der Aufgaben, womit dieses Buch dem Nachbereiten vo...

This book provides an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus. Supplementary problems in each chapter will challenge and excite the reader, ideal for both graduate and undergraduate mathematics and theoretical physics students. The coverage includes systems of linear equations, linear differential equations, integration and matrices, Kronecker product and vec-operation as well as functions of matrices. Furthermore, specialized topics...

A monumental accomplishment in the history of non-Western mathematics, The Chinese Roots of Linear Algebra explains the fundamentally visual way Chinese mathematicians understood and solved mathematical problems. It argues convincingly that what the West "discovered" in the sixteenth and seventeenth centuries had already been known to the Chinese for 1,000 years. Accomplished historian and Chinese-language scholar Roger Hart examines Nine Chapters of Mathematical Arts-the classic ancient Chin...

Im vorliegenden Lehrbuch werden die Grundlagen der Linearen Algebra im Detail vorgestellt: Nachdem die grundlegenden Strukturen der Mathematik - die Gruppen, Ringe und Koerper - eingefuhrt sind, werden Vektorraume und lineare Abbildungen zwischen ihnen ausfuhrlich vorgestellt. Wichtige Normalformen werden ebenso diskutiert wie die Determinante und das Problem der Diagonalisierung. Abschliessend werden die Theorien der euklidischen und unitaren Vektorraume parallel entwickelt. Die formalen Aspekt...

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers...

"Integers" is a refereedonline journal devoted to research in the area of combinatorial number theory. It publishes original research articles in combinatorics and number theory. Topics covered by the journal include additive number theory, multiplicative number theory, sequences and sets, extremal combinatorics, Ramsey theory, elementary number theory, classical combinatorial problems, hypergraphs, and probabilistic number theory. Integers also houses a combinatorial games section. This work...

Modern imaging techniques and computational simulations yield complex multi-valued data that require higher-order mathematical descriptors. This book addresses topics of importance when dealing with such data, including frameworks for image processing, visualization and statistical analysis of higher-order descriptors. It also provides examples of the successful use of higher-order descriptors in specific applications and a glimpse of the next generation of diffusion MRI. To do so, it combines c...

All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combin...

Accosiative rings and algebras are very interesting algebraic structures. In a strict sense, the theory of algebras (in particular, noncommutative algebras) originated fromasingleexample,namelythequaternions,createdbySirWilliamR.Hamilton in1843. Thiswasthe?rstexampleofanoncommutative"numbersystem". During thenextfortyyearsmathematiciansintroducedotherexamplesofnoncommutative algebras, began to bring some order into them and to single out certain types of algebras for special attention. Thus, low...

This edition strives to develop students' geometric intuition as a foundation for learning the concepts of span and linear independence. Applications are integrated throughout to illustrate the mathematics and to motivate the student. Numerical ideas and concepts using the computer are interspersed throughout the text; instructors can use these at their discretion. This textbook allows the instructor considerable flexibility to choose the applications and numerical topics to be covered according...

This book developed from the need to teach a linear algebra course to students focused on data science and bioinformatics programs. These students tend not to realize the importance of linear algebra in applied sciences, since traditional linear algebra courses tend to cover mathematical contexts but not the computational aspect of linear algebra or its applications to data science and bioinformatics. The author presents the topics in a traditional course, yet offers lectures as well as lab ex...

O objetivo deste livro e o de fornecer as primeiras ferramentas matematicas associadas a Algebra Linear. O texto foi elaborado por um matematico que procurou "sair do seu personagem" para vir ao encontro de um publico amplo. O desafio e o de tornar acessivel a todos, os primeiros fundamentos e as primeiras tecnicas de um saber fundamental para a ciencia e a tecnologia. Com esse intuito, o autor escolheu escreve-lo em um estilo nao tradicional e o enriqueceu nao somente com exercicios, mas tamb...