线性算子

Hacker News 上怎么说

• graycat · 2020 年

  ……让她解释了她当时用的硬件以及她是怎么充分榨干其性能的！我记得她嫁给了纽约大学柯朗研究所的 Jack Schwartz，也就是写出《Linear Operators》的 Nelson Dunford 和 Jacob T. Schwartz 里的那位。

  …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.

• graycat · 2017 年

  ……m x n 的矩阵 A、n x 1 的向量 x、n x 1 的向量 y，以及数 p 和 q，我们有 A(px + qy) = (pAx) + (qAy)，这表明 A 是线性的，或者说是一个线性算子——在微积分中，微分和积分也都是线性算子。Dunford 和 Schwartz 写过一本大部头巨著《Linear Operators》，也就是泛函分析，在那里我们讨论、分析的点，实际上就是函数。所以，极其重大的特例是……

  …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…

• graycat · 2017 年

  ……交换两个求和符号的顺序，而且这个结论是可以推广的。矩阵乘积是线性系统中线性算子的第一个极佳范例。现实世界中到处都是线性系统。关于线性算子的资料非常多，比如 Dunford 和 Schwartz 的《Linear Operators》。电子工程、声学以及量子力学里线性算子无处不在。要为现实世界建模，做 ML、AL、数据科学……

  …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, ...,…

• graycat · 2017 年

  ……线性性的各种形式贯穿了应用数学的绝大部分，比如傅里叶分析、快速傅里叶变换、X 射线衍射、巴拿赫空间、希尔伯特空间，经典的 Dunford 和 Schwartz 写的《Linear Operators》等等。简单来说，巴拿赫空间就是一个标量为实数或复数的向量空间，上面定义了范数（也就是距离的定义），并且该空间在这个范数下是完备的。完备……

  …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…

• graycat · 2017 年

  ……m x n 的矩阵 A、n x 1 的向量 x、n x 1 的向量 y，以及数 p 和 q，我们有 A(px + qy) = (pAx) + (qAy)，这表明 A 是线性的，或者说是一个线性算子——在微积分中，微分和积分也都是线性算子。Dunford 和 Schwartz 写过一本大部头巨著《Linear Operators》，也就是泛函分析，在那里我们讨论、分析的点，实际上就是函数。所以，极其重大的特例是……

  …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…

• nicklaf · 2018 年

  G.C. Rota 当年在耶鲁读研究生时，被指派去帮 Dunford 和 Schwartz 校验《Linear Operators》（当时还是手稿）里的习题，结果发现自己有一道题死活解不出来：几个小时过去了，感到颇为沮丧，我们大家……

  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…

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