n-Linear Algebra of type I and its applications
From MaRDI portal
Publication:5505133
zbMATH Open1153.15300arXiv0812.1950MaRDI QIDQ5505133
W. B. Vasantha Kandasamy, Florentin Smarandache
Publication date: 23 January 2009
Abstract: With the advent of computers, one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure, namely, n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of n-vector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several related results which are analogues of the classical linear algebra theorems. In case of n-vector spaces, we can define several types of linear transformations. The notion of n-best approximations can be used for error correction in coding theory. The notion of n-eigen values can be used in deterministic modal superposition principle for undamped structures, which can find its applications in finite element analysis of mechanical structures with uncertain parameters. Further, it is suggested that the concept of n-matrices can be used in real world problems which adopts fuzzy models like Fuzzy Cognitive Maps, Fuzzy Relational Equations and Bidirectional Associative Memories. The applications of these algebraic structures are given in the third chapter. The fourth chapter suggests problems to further a reader's understanding of the subject.
Full work available at URL: https://arxiv.org/abs/0812.1950
Research exposition (monographs, survey articles) pertaining to computer science (68-02) Research exposition (monographs, survey articles) pertaining to linear algebra (15-02)
This page was built for publication: n-Linear Algebra of type I and its applications
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5505133)
