Gourt > Science > Math > Numerical Analysis > Linear Algebra
Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear transformations, and systems of linear equations in finite dimensions. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry and it is generalized in operator theory. It has extensive applications in the natural sciences and the social sciences, since nonlinear models can often be approximated by a linear model.
History
The history of modern linear algebra dates back to the years 1843 and 1844. In 1843, William Rowan Hamilton (from whom the term vector stems) discovered the quaternions. In 1844, Hermann Grassmann published his book Die lineale Ausdehnungslehre (see References). Arthur Cayley introduced matrices, one of the most fundamental linear algebraic ideas, in 1857. These early references belie the fact that linear algebra is mainly a development of the twentieth century: the number-like objects matrices were hard to place before the development of ring theory in abstract algebra. With the coming of special relativity many practioners gained appreciation of the subtleties of linear algebra. Furthermore, the routine application of Cramer's rule to solve Partial differential equations led to inclusion of linear algebra in standard coursework at universities. For instance, E.T. Copson wrote:
More on [ Linear algebra ]
Linear Algebra :: Source Code
Linear Algebra :: Algebra
Sex and the Smithie - The Sophian
Fri, 05 Sep 2008 14:43:28 -0000
Sex and the SmithieThe Sophian, MA - 14 hours agoI would never take Linear Algebra, no matter what horizons might be broadened, just as some would never take Contemporary Literary Theory. In the same vein, ...
Math night slated for parents - Joliet Herald News
Fri, 05 Sep 2008 09:13:11 -0000
Math night slated for parentsJoliet Herald News, IL - 20 hours ago... solving equations and linear equations. Algebra students will be taught the high school algebra course, which is a broad introduction to algebra. ...
Accelerator Appliance suits technical computing applications. - ThomasNet Industrial News Room
Fri, 05 Sep 2008 17:28:46 -0000
Accelerator Appliance suits technical computing applications.ThomasNet Industrial News Room, NY - 12 hours ago... separate 1U servers by up to 3.5 times for scalable dense linear algebra related applications, and by 6.5 times for Black Scholes-related applications. ...
OptimaNumerics to Support NVIDIA Tesla GPU Platform - LinuxElectrons
Sun, 24 Aug 2008 00:06:23 -0000
OptimaNumerics to Support NVIDIA Tesla GPU PlatformLinuxElectrons, TX - Aug 23, 2008OptimaNumerics Libraries, with linear algebra, parallel linear algebra and parallel random number generators modules, provide high performance versions of ...
Math whizzes' academic talent shines - Press-Enterprise
Sun, 24 Aug 2008 06:20:44 -0000
Math whizzes' academic talent shinesPress-Enterprise, CA - Aug 23, 2008They received credit from Cal State San Marcos for calculus D and linear algebra. Math teacher Brian May's students in a new course on differential ...
Pinpointing Genetic Variations In European Americans - Science Daily (press release)
Thu, 07 Aug 2008 18:48:18 -0000
Pinpointing Genetic Variations In European AmericansScience Daily (press release) - Aug 7, 2008The team used linear algebra to find patterns in the highly diverse data. When the data sets were analyzed using the proposed algorithms, these patterns ...
Bibliography on Sparse Linear Systems and Related Areas of Computation - With emphasis on Computational Linear Algebra, High Performance Computing, Mathematical Programming and Graph Theory. Searchable.
Meta Description: [ Bibliography on the Solution of Sparse Linear Systems and Related Areas of Computation. This bibliography is a part of the Computer Science Bibliography Collection. ]
Bibliography on the Solution of Sparse Linear Systems and Related Areas of Computation - More than 2000 selected references, covering the solution of sparse linear systems and related areas of computation, including: computational linear algebra, high performance computing, mathematical programming and graph theory.
Meta Description: [ This bibliographic list of references was originally compiled during the elaboration of my PhD thesis, and has been gradually expanded since them, counting now with more than selected references, covering the solution of sparse linear systems and related areas of computation, including computatio... ]
Information Base on Sparse Linear Systems and Matrix Computations - Bibliographic references, links and search interfaces.
Meta Description: [ This page provides a base of Bibliographic
References and Web Links related to the Solution of Sparse Systems of
Linear Equations, additionally providing links to other bases on Related Areas
of Scientific Computing, with emphasis on Computational Linear Algebra,
High Performance Computing and Ma... ]
Matrix Market - A visual repository of test data for use in comparative studies of algorithms for numerical linear algebra, featuring nearly 500 sparse matrices from a variety of applications, as well as matrix generation tools and services.
Meta Description: [ A repository of matrix test data for use in comparative studies
of algorithms. The matrices have been taken from problems in
linear systems, least squares, and eigenvalue calculations in a
wide variety of scientific and engineering disciplines. Includes
... ]
Preconditioned Eigensolvers - Software, papers, and references.
Pseudospectra Gateway - The pseudospectrum of a matrix provides information about the behavior of the eigenvalues of A when A is subject to perturbations. Links to other resources.
Sparse Matrix Collection (T. Davis) - A collection of large sparse matrices from many scientific disciplines with links and software pieces to operate on matrix data structures.
| .edu/terms More courses at http://ocw.mit.edu ... equations vector algebra linear mit opencourseware eigenvalues ... | |
| Next Video | |
