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With respect to general linear maps, linear endomorphisms and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other part of mathematics.
The factors of the minimal polynomial m are the elementary divisors of the largest degree corresponding to distinct eigenvalues. The degree of an elementary divisor is the size of the corresponding Jordan block, therefore the dimension of the corresponding invariant subspace. If all elementary divisors are linear, A is diagonalizable.
Download as PDF; Printable version; ... This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps ...
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.
In mathematics, an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix.The elementary matrices generate the general linear group GL n (F) when F is a field.
Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers. It is typically taught to secondary school students and at introductory college level in the United States, [4] and builds on their understanding of arithmetic. The use of variables to denote quantities allows ...
Linear systems are a fundamental part of linear algebra, a subject used in most modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra , and play a prominent role in engineering , physics , chemistry , computer science , and economics .
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