Linear Algebra

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).

Linear algebra notes

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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.

arXiv (Cornell University), 2023

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...