Circulant Matrices 2nd Edition by Philip J. Davis (PDF)

Description

From the Preface: “Twenty years ago, noting that the basic facts about circulant matrices and its relationship to the Discrete Fourier Transform were rediscovered over and over again, I thought it might be worthwhile to publish a small book in which these facts were summarized (1979). What I did not realize was the extent to which in the years to come circulant matrices would play a role in applications and the extent to which algebraists, numerical analysts, combinatorialists and physicists would push forward the development of generalized circulants. Such matrices are now often seen as special instances of structured or patterned matrices … The outgrowth of the simple notion of a circulant matrix has therefore been both vast and profound. Readers who are interested in applications or generalizations of circulants beyond what is given in this volume may find a … list of publications (and their bibliographies) to be of use.” Second edition, with historical remarks and several additional references

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Philip J. Davis, the author of Circulant Matrices, is a well known, most exceptional, talented, applied mathematician, a PhD graduate of Harvard University, a prolific writer of books, essays, reviews, and papers, a winner of the Chauvenet prize for expository skills in mathematical writing, a popular book reviewer for SIAM News–his monthly column is a not to be missed, must read–and, finally, in my opinion, a true “polymath” for his cross-cultural writings in a book like “The Mathematical Experience” (with R. Hersh) and his fictional works.That said, what about Davis’ present book? Why only four stars and not five for Circulant Matrices? Well, this 1979 book of some 250 pages gets a minor ding and loses one star only because the typography is less than aesthetically pleasing–to put it mildly–and in a few instances, is downright annoying, because the printer run has sent several skewed lines sliding nearly off the page. The book deserves to be republished with its matrix notation converted to more pleasing typefaces. Such an improvement is easily achieved nowadays with software from Microsoft, Design Science, and Adobe, all of which neatly and pleasingly handles mathematical glyphs and similar symbols, and also allows distillation of Word files into high speed printer-ready documents.That said, the content is exactly what matrix addicted persons are looking for to satisfy their appetites. Because I am such a person, completely addicted to learning more about matrices, in all their shapes, forms, and properties,Dr. Davis is exactly the sort of matrix maven who can and has satisfied my cravings. He has done so in Circulant Matrices. Here are a few examples. Want a nice, straightforward proof of the complex singular value decomposition? There it is, starting on page 50. Want to learn about the complex Fourier matrix and its connection to the Fast Fourier Transform (FFT). It’s all there, starting on page 31. Of course most everything you would want to know about the generic circulant matrix form is also there, spread through multiple chapters.If you like matrices, buy this gem of a book, read it, and learn why circulant matrices are “really cool stuff”.Lewis H. Robinson.

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