Background from linear algebra

Keyword(s):  
Author(s):  
Mihály Bakonyi ◽  
Hugo J. Woerdeman

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than two hundred exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to six hundred references from books and journals from a wide variety of disciplines.


Author(s):  
Leiba Rodman

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.


Author(s):  
J. H. Wilkinson ◽  
C. Reinsch
Keyword(s):  

2018 ◽  
Vol 1 (1) ◽  
pp. 46-54
Author(s):  
Besse Intan Permatasari

This study aims to determine whether there is an influence of creativity on mathematics learning outcomes of students of Mathematics Education in University of Balikpapan Study Program on Linear Algebra Courses. The approach used is a quantitative approach with ex post facto research type. The population of this research is all students of Mathematics Education Study Program Linear Algebra Course in the School Year 2017/2018, which are 49 students. Samples were chosen randomly are 25 students. The results showed that there is a positive and significant effect on student learning outcomes in Linear Algebra Subject


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