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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.
C++ template library; binds to optimized BLAS such as the Intel MKL; Includes matrix decompositions, non-linear solvers, and machine learning tooling Eigen: Benoît Jacob C++ 2008 3.4.0 / 08.2021 Free MPL2: Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. Fastor [5]
Version 1.0 was released in Dec 2006. [3] Eigen is implemented using the expression templates metaprogramming technique, meaning it builds expression trees at compile time and generates custom code to evaluate these. Using expression templates and a cost model of floating point operations, the library performs its own loop unrolling and ...
Expression templates have been found especially useful by the authors of libraries for linear algebra, that is, for dealing with vectors and matrices of numbers. Among libraries employing expression template are Dlib , Armadillo , Blaze , [ 5 ] Blitz++ , [ 6 ] Boost uBLAS, [ 7 ] Eigen , [ 8 ] POOMA, [ 9 ] Stan Math Library , [ 10 ] and xtensor ...
To change this template's initial visibility, the |state= parameter may be used: {{ Linear algebra | state = collapsed }} will show the template collapsed, i.e. hidden apart from its title bar. {{ Linear algebra | state = expanded }} will show the template expanded, i.e. fully visible.
This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices. Linear equations
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Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis.