Academia.edu no longer supports Internet Explorer.
To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser.
…
681 pages
1 file
Lecture notes I wrote for the section of MATH 110 Linear Algebra I taught at University of California, Berkeley during Summer 2017. Should be considered in "beta". If you do find any mistakes, anything from simple typos to egregious mathematical errors, please do let me know. Comments and suggestions welcome as well =) [email protected]
an asterisk can be omitted without loss of continuity but may be required for later optional sections. See each indicated section for dependency information.
These notes were written as a part of a graduate level course on transform theory offered at King's College London during 2002 and 2003. The material is heavily indebt to the excellent textbook by Gilbert Strang [1], which the reader is referred to for a more complete description of the material; for a more in-depth coverage, the reader is referred to [2–6].
2009
in Canton New York where he has taught undergraduate mathematics for 25 years. St. Lawrence University is a small Liberal Arts College in upstate New York that prides itself in the close interaction that exists between students and faculty. It is this many years of working closely with students that has shaped this text in Linear Algebra and the other texts he has written. He received his Ph.D. in Pure Mathematics from Kent State University in 1979. Dr. DeFranza has coauthored PRECALCULUS, Fourth Edition and two other texts in single variable and multivariable calculus. Dr. DeFranza has also published a dozen research articles in the areas of Sequence Spaces and Classical Summability Theory. Jim is married and has two children David and Sara. Jim and his wife Regan live outside of Canton New York in a 150 year old farm house.
Some basic ideas from linear algebra play an essential role in our subject, so I'm o¤ering this summary as a reference. These notes won't substitute for a proper textbook. In particular, I won't give proofs of anything here. Nevertheless, I hope they will be of some use. I may add to these notes later the semester. (I won't add to them earlier).
To order books or for customer service call 1-800-CALL-WILEY (225-5945).
Library of Congress Cataloging-in-Publication Data Lang, Serge Linear algebra. (Undergraduate texts in mathematics) Includes bibliographical references and index.
The American Mathematical Monthly, 1969
The purpose of this first set of lecture notes is to summarize background material on linear algebra and analysis that is used throughout the course. Proofs of most of the stated facts may be found in the references listed at the end of the notes. It is my intention that this first set of notes will mostly serve as a useful reference later in the course.
2007
S Subadditive and Superadditive Inequalities T. Ando Faculty of Economics Hokusei Gakuen University Sapporo 004-8631 Japan [email protected] Key identifying words: subadditive and superadditve inequalities, operator-monotone function. It is known that if f(t) is a non-negative, operator-monotone (that is, matrix-monotone of all orders) function on [0;1) then the inequality jjjf(A+B) f(A)jjj jjjf(B)jjj holds for every pair of positive semi-de nite matrices A;B and every unitarily invariant norm jjj jjj. In this talk we discuss inequalities of the form jjjf(A+B)jjj jjjf(A) + f(B)jjj: Diagonals of Matrices Rajendra Bhatia Indian Statistical Institute New Delhi 110 016 India [email protected] Key identifying words: diagonal, norm, Fourier series, inequalities The diagonal of a matrix can be expressed as an average over unitary conjugates of the matrix.We will display such expressions for the main diagonal and other diagonals parallel to it.This leads to some interesting sharp bounds...
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.
Linear Algebra and its Applications, 1992