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Author: Piotr Krylov
Publisher: Springer
ISBN: 3319539078
Category : Mathematics
Languages : en
Pages : 165
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Book Description
This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a solid understanding of basic algebra.
Author: Piotr Krylov
Publisher: Springer
ISBN: 3319539078
Category : Mathematics
Languages : en
Pages : 165
Get Book Here
Book Description
This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a solid understanding of basic algebra.
Author: Stephen Boyd
Publisher: Cambridge University Press
ISBN: 1316518965
Category : Business & Economics
Languages : en
Pages : 477
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Book Description
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author: Pease
Publisher: Academic Press
ISBN: 0080955223
Category : Mathematics
Languages : en
Pages : 425
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Book Description
Methods of Matrix Algebra
Author: Zhiping Shi
Publisher: Springer Nature
ISBN: 9811572615
Category : Mathematics
Languages : en
Pages : 172
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Book Description
This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.
Author: Jacob T. Schwartz
Publisher: Courier Corporation
ISBN: 9780486420004
Category : Mathematics
Languages : en
Pages : 198
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Book Description
Concise undergraduate text focuses on problem solving, rather than elaborate proofs. The first three chapters present the basics of matrices, including addition, multiplication, and division. In later chapters the author introduces vectors and shows how to use vectors and matrices to solve systems of linear equations. 1961 edition. 20 black-and-white illustrations.
Author: Daniel Talbot Finkbeiner
Publisher:
ISBN:
Category : Algebras, Linear
Languages : en
Pages : 0
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Book Description
Author: Richard A. Brualdi
Publisher: Cambridge University Press
ISBN: 9780521322652
Category : Mathematics
Languages : en
Pages : 384
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Book Description
This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves.
Author: Daizhan Cheng
Publisher: Academic Press
ISBN: 0128178027
Category : Mathematics
Languages : en
Pages : 364
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Book Description
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product (STP), a generalized matrix product that extends the conventional matrix product to two matrices of arbitrary dimensions. Dimension-varying systems feature prominently across many disciplines, and through innovative applications its newly developed theory can revolutionize large data systems such as genomics and biosystems, deep learning, IT, and information-based engineering applications. Provides, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems. Offers potential applications to the analysis and control of new dimension-varying systems. Investigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid of matrices with arbitrary dimensions.
Author: Vadim Olshevsky
Publisher: American Mathematical Soc.
ISBN: 0821819216
Category : Matrices
Languages : en
Pages : 346
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Book Description
"The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numberical issues. The presentation fully illustrates the fact that the technicques of engineers, mathematicisn, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices"--Back cover.
Author: Francesco Aldo Costabile
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110757249
Category : Mathematics
Languages : en
Pages : 526
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Book Description
Polynomials are useful mathematical tools. They are simply defined and can be calculated quickly on computer systems. They can be differentiated and integrated easily and can be pieced together to form spline curves. After Weierstrass approximation Theorem, polynomial sequences have acquired considerable importance not only in the various branches of Mathematics, but also in Physics, Chemistry and Engineering disciplines. There is a wide literature on specific polynomial sequences. But there is no literature that attempts a systematic exposition of the main basic methods for the study of a generic polynomial sequence and, at the same time, gives an overview of the main polynomial classes and related applications, at least in numerical analysis. In this book, through an elementary matrix calculus-based approach, an attempt is made to fill this gap by exposing dated and very recent results, both theoretical and applied.
