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English: Linear Algebra by Jim Hefferon, along with its answers to exercises, is a text for a first undergraduate course. It is Free. Use it as the main book, as a supplement, or for independent study.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
He retired on May 15, 2023 after giving his final Linear Algebra and Learning from Data [6] lecture at MIT. [ 7 ] Strang's teaching has focused on linear algebra which has helped the subject become essential for students of many majors.
Download as PDF; Printable version; ... Linear algebra is the branch of mathematics concerning linear equations such as: ... MIT Linear Algebra Video Lectures, ...
Double-precision arithmetic in Macsyma (on a PC version) was about six times slower than Fortran. Also Macsyma's matrices were implemented as lists of lists, which cost another factor of perhaps 5–10 in speed for key algorithms. Macsyma did not have many of the basic algorithms of numerical linear algebra, such as LU decomposition.
Magma includes the KANT computer algebra system for comprehensive computations in algebraic number fields. A special type also allows one to compute in the algebraic closure of a field. Module theory and linear algebra; Magma contains asymptotically fast algorithms for all fundamental dense matrix operations, such as Strassen multiplication ...
The Steinitz exchange lemma is a basic theorem in linear algebra used, for example, to show that any two bases for a finite-dimensional vector space have the same number of elements. The result is named after the German mathematician Ernst Steinitz .
The first branch of algebraic graph theory involves the study of graphs in connection with linear algebra.Especially, it studies the spectrum of the adjacency matrix, or the Laplacian matrix of a graph (this part of algebraic graph theory is also called spectral graph theory).
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