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Titlebook: Linear Algebra and Group Theory for Physicists and Engineers; Yair Shapira Textbook 2023Latest edition The Editor(s) (if applicable) and T

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发表于 2025-3-21 20:02:47 | 显示全部楼层 |阅读模式
书目名称Linear Algebra and Group Theory for Physicists and Engineers
编辑Yair Shapira
视频video
概述Introduces linear algebra and group theory together for a more intuitive understanding of applied mathematics.Utilizes an interdisciplinary approach to appeal to a broad scientific audience.Provides a
图书封面Titlebook: Linear Algebra and Group Theory for Physicists and Engineers;  Yair Shapira Textbook 2023Latest edition The Editor(s) (if applicable) and T
描述This textbook demonstrates the strong interconnections between linear algebra and group theory by presenting them simultaneously, a pedagogical strategy ideal for an interdisciplinary audience. Being approached together at the same time, these two topics complete one another, allowing students to attain a deeper understanding of both subjects. The opening chapters introduce linear algebra with applications to mechanics and statistics, followed by group theory with applications to projective geometry. Then, high-order finite elements are presented to design a regular mesh and assemble the stiffness and mass matrices in advanced applications in quantum chemistry and general relativity..This text is ideal for undergraduates majoring in engineering, physics, chemistry, computer science, or applied mathematics. It is mostly self-contained—readers should only be familiar with elementary calculus. There are numerous exercises, with hints or full solutions provided. A series of roadmaps are also provided to help instructors choose the optimal teaching approach for their discipline..The second edition has been revised and updated throughout and includes new material on the Jordan form, the
出版日期Textbook 2023Latest edition
关键词Group theory; Linear algebra; High dimensional vectors; Fourier matrices; Markov chain; Quantum mechanics
版次2
doihttps://doi.org/10.1007/978-3-031-22422-5
isbn_softcover978-3-031-22424-9
isbn_ebook978-3-031-22422-5
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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发表于 2025-3-21 22:57:39 | 显示全部楼层
Vectors and MatricesWhat is a vector? It is a finite list of (real) numbers: scalars or components.
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Quantum Mechanics: Algebraic Point of ViewMatrices have two algebraic operations. Thanks to addition, they make a new linear space. Thanks to multiplication, they also form a group: the nonsingular matrices.
发表于 2025-3-22 21:23:05 | 显示全部楼层
Polynomials and Their GradientThe polynomial is a special kind of function, easy to deal with. We start with a polynomial of one independent variable: .. This is an algebraic object: it supports addition, multiplication, and composition. Still, it is also a function that returns a value. To calculate it, we introduce the efficient Horner algorithm.
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