Matrix Computations and Semiseparable Matrices: Linear Systems (Volume 1)
In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices.
This is a book of applied mathematical proofs. If you have seen a mathematical result, if you want to know why the result is so, you can look for the proof here. The book's purpose is to convey the essential ideas underlying the derivations of a large number of mathematical results useful in the modeling of physical systems. To this end, the book emphasizes main threads of mathematical argument and the motivation underlying the main threads, deemphasizing formal mathematical rigor.
This text is appropriate for students from across the engineering and science disciplines. Topics include: Periodicity and Fourier series; The Fourier transform and its basic properties; Convolution and its applications; Distributions and their Fourier transforms; Sampling and interpolation; Linear systems; The discrete Fourier transform; Higher dimensional Fourier transforms and applications.
For readers with a basic graduate level background in algebra, these ten articles provide a readable introduction to three major interrelated subjects of noncommutative algebra. The theme is the interplay between group theory and ring theory, dealing specifically with group rings, crossed products, and the Galois theory of rings. The author has carefully included most definitions, to keep the required background minimal. Each article contains a selection of results on the given topic, a limited number of proofs or sketches, and at least a few open problems
This monumental book was specially designed to make mathematics more accessible to the inexperienced. It comprises nontechnical essays on every aspect of the vast subject, including articles by and about scores of eminent mathematicians, as well as literary figures, economists, biologists, and many other eminent thinkers. This unique compendium includes the work of Archimedes, Galileo, Descartes, Newton, Gregor Mendel, John Maynard Keynes, Lewis Carroll, Bertrand Russell, John von Neumann, and many others.
