The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank Google's ranking algorithm , and cancer detection from cell features.
A companion web site, codingthematrix. Most of the assignments can be auto-graded online. Orthogonalization least squares, linear regression, compensating for inaccurate measurements by using more measurements, applying least-squares to the machine-learning problem , The SVD multiplying a vector by a rank-one or low-rank matrix, Frobenius norm , Nov.
Orthogonalization matrix form, using orthogonalization for closest vector, basis, subset-basis, and null space basis , Nov. Gaussian Elimination recording transformations, factoring integers, authentication , Oct. Web icon An illustration of a computer application window Wayback Machine Texts icon An illustration of an open book. Books Video icon An illustration of two cells of a film strip. Video Audio icon An illustration of an audio speaker. Audio Software icon An illustration of a 3.
Software Images icon An illustration of two photographs. Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses. About the author Paul Orland is a programmer, software entrepreneur, and math enthusiast. He is co-founder of Tachyus, a start-up building predictive analytics software for the energy industry. You can find him online at www. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix.
Recently, many other algorithms of this type were discovered, and the theory of structured matrices emerged. This volume contains 22 survey and research papers devoted to a variety of theoretical and practical aspects of the design of fast algorithms for structured matrices and related issues. Included are several papers containing various affirmative and negative results in this direction. The theory of rational interpolation is one of the excellent sources providing intuition and methods to design fast algorithms.
The volume contains several computational and theoretical papers on the topic. There are several papers on new applications of structured matrices, e. The book is suitable for mathematicians, engineers, and numerical analysts who design, study, and use fast computational algorithms based on the theory of structured matri. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research.
The book features an accessibl. Author : Joaquim Borges Publisher: Univ. The conference had great acceptance within the community of coding theory and cryptography researchers. At that moment, and also nowadays, there are not many international workshops about these topics, at least if we compare with other mathematical and engineering subjects of research.
Therefore, the general desire was to continue with more Castle Meetings. However, the following conference did not take place until In that case, the conference was called II International Castle Meeting on Coding Theory and Applications allowing more topics related to coding theory apart from cryptography.
Such conference took place at Mota Castle again and the number of participants was similar to the previous edition. The number of communications has increased and a number of selected papers will be published in a special issue of the journal Designs, Codes and Cryptography. As in the previous editions, the conference has been of high level with notorious invited speakers and scientic committee members.
It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations. It is also useful for those who are interested in supplementary reading at a higher level.
The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text.
In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas.
Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.
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