Free Ebook A Survey of Matrix Theory and Matrix Inequalities (Dover Books on Mathematics)
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A Survey of Matrix Theory and Matrix Inequalities (Dover Books on Mathematics)
Free Ebook A Survey of Matrix Theory and Matrix Inequalities (Dover Books on Mathematics)
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Product details
Series: Dover Books on Mathematics
Paperback: 208 pages
Publisher: Dover Publications; Revised ed. edition (September 16, 2010)
Language: English
ISBN-10: 048667102X
ISBN-13: 978-0486671024
Product Dimensions:
5.4 x 0.4 x 8.4 inches
Shipping Weight: 4 ounces (View shipping rates and policies)
Average Customer Review:
4.6 out of 5 stars
4 customer reviews
Amazon Best Sellers Rank:
#1,560,681 in Books (See Top 100 in Books)
Although the text is not up-to-date (e.g., it states on pp. 129-130 that the van der Waerden conjecture on the permanent of stochastic matrices is still unresolved!), most classical results in matrix theory and analysis is presented in an unpretentious style and with due credit to the original contributions. Proofs are given with only a modicum of rigor for the more important and general theorems and some exemples (but not many) are worked out to illustrate the possibilities and limitations of the techniques.On the downside, the book is typeset in a small type that makes it difficult to discern sub-subscripts and superscripts in some expressions. I am not nitpicking here: sometimes you cannot affirm if that index is an "i" or a "t", and if it is an "i_t" or a "t_i" it only gets worse. Given its enduring value, a new printing in a slightly larger font, say, 1pt up, would be a good service to its readership.I prefer this title to the much more expensive (and not that much up-to-date) book by Horn & Johnson. If you cannot afford both, go with Marcus & Minc. I am not rating it 5 stars because of (i) its age, (ii) its annoying typeset (a minor issue, actually), and (iii) the typos, of the confusing kind. Otherwise, for the practicing scientist and engineer and for students looking for a cheap reference, I can only recommend this book.
I got this book very quickly. But I think this book just includes some important theorems. It does not include how to prove them.
This book is not really a review of matrix theory; the focus is on inequalities, mainly for PD matrices, convex functions and eigenvalue problems. The book tries to present a general framework, a-la Hardy, but is not quite as successful. Nevertheless, if you need to find that elusive inequality that you saw in undergraduate, this book will likely contain it. This book should be on every mathematical researcher's shelf.
Each section starts with a set of necessary definitions. Then, theorems are stated without proof---therefore, the it can also be used as an exercise book. One can go to a section of interest and try to prove some of the theorems listed there.
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