Linear operators
by Nelson Dunford, Neilson Dunford, Jacob T. Schwartz, Nelson James Dunford, W. G. Bade, Robert G. Bartle · first published 1957
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2013–2020first – last mentioned
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…got her to explain the hardware she was using and how she was exploiting it! As I recall, she was married to Jack Schwartz at Courant Institute of NYU and as in Nelson Dunford and Jacob T. Schwartz, Linear Operators.
on “Frances Allen has died” ↗…m x n A, n x 1 x, n x 1 y, and numbers p and q, we have A(px + qy) = (pAx) + (qAy) which says that A is linear or a linear operator -- in calculus, both differentiation and integration are also linear operators. There is a huge book Linear Operators by Dunford and Schwartz, that is, functional analysis, that is where the points we are talking about, analyzing, actually functions. So, biggie special cases are…
on “No bullshit guide to linear algebra – v2” ↗…interchanging the order two summation signs, and that fact generalizes. Matrix product is the first good example of a linear operator in a linear system. The world is awash in linear systems. There is a lot on linear operators, e.g., Dunford and Schwartz, Linear Operators. Electronic engineering, acoustics, and quantum mechanics are awash in linear operators. To build a model of the real world, for ML, AL, data science, ...,…
on “Ask HN: What maths are critical to pursuing ML/AI?” ↗…version of linearity takes one through much of all of applied math, e.g., Fourier analysis, the fast Fourier transform, X-ray diffraction, Banach space, Hilbert space, the classic Dunford and Schwartz, Linear Operators, etc. So, a Banach space is just a vector space where the scalars are the real or complex numbers, there is a norm, that is, a definition of distance, and the space is complete in that norm. Complete…
on “Confession as an AI researcher; seeking advice” ↗…m x n A, n x 1 x, n x 1 y, and numbers p and q, we have A(px + qy) = (pAx) + (qAy) which says that A is linear or a linear operator -- in calculus, both differentiation and integration are also linear operators. There is a huge book Linear Operators by Dunford and Schwartz, that is, functional analysis, that is where the points we are talking about, analyzing, actually functions. So, biggie special cases are…
on “No bullshit guide to linear algebra – v2” ↗G.C. Rota, on being assigned to help check the problems of Linear Operators for Dunford and Schwartz as a graduate student at Yale (while it was still a manuscript), but finding himself unable to solve one of the problems: After a few hours, feeling somewhat downcast, we all…
on “Robert Langlands, Mathematical Visionary, Wins the Abel Prize” ↗…interleaved memory or some such, etc.! That was really getting into the details! She was one of the very few women I ever saw in a STEM subject and good at it. Her husband was Jack Schwartz of the fundamental 'Linear Operators' with Nelson Dunford, as I recall, at Yale. Schwartz was long at Courant and did a programming language SETL, 'set language', for allowing programming via essentially set theory notation.
on “Stop complaining about the lack of women in tech” ↗If you're frequently passing by a university library, see if they have a shelf where they sell old books. Mine does, and I've scored some sweet stuff there, e.g. Dunford and Schwartz' Linear Operators Part 1 & 2 together for $8, which looks to be $150 + shipping for used copies from Amazon ($400 new). As you can probably tell, there's an arb opportunity there as well.
on “Automated reasoning in F#, Scala, Haskell, C++, and Julia” ↗…sonar, radar, and radio astronomy, seismology, quantum mechanics, yes, error correcting codes, linear ordinary and partial differential equations, ..., and then Nelson Dunford and Jacob T. Schwartz, Linear Operators Part I: General Theory, ISBN 0-470-22605-6, Interscience, New York.
on “An Intuitive Guide to Linear Algebra (2012)” ↗