Numerical linear algebra

MATLAB (Matrix Laboratory) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.

collection of linear equations involving the same set of variables

algorithm for solving systems of linear equations

special kind of square matrix

mathematical operation in linear algebra

high-performance dynamic programming language

inverse image of zero under a linear map

matrix decomposition

Mathematical concept

iterative method used to solve a linear system of equations

Mathcad is computer software for the verification, validation, documentation and re-use of mathematical calculations in engineering and science, notably mechanical, chemical, electrical, and civil engineering. Released in 1986 for MS-DOS, it introduced live editing (WYSIWYG) of typeset mathematical notation in an interactive notebook, combined with automatic computations. It was originally developed by Mathsoft, and since 2006 has been a product of Parametric Technology Corporation.

matrix decomposition

matrix decomposition

iterative method used to solve a linear system of equations

subfield of numerical analysis and a type of linear algebra

LINPACK is a software library for performing numerical linear algebra on digital computers.

matrix decomposition

linear transformation that describes a reflection about a plane or hyperplane containing the origin

square matrix whose entries are unit fractions of special form

possible form of a matrix

matrix in which the magnitude of the diagonal entry in a row is no less than the sum of the magnitudes of the nondiagonal entries in that row

method to compute systems of linear equations whose matrix is symmetric positive-definite

matrix in which each row is rotated one position to the right from the previous row

LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008). The routines handle both real and complex matrices in both single and double precision. LAPACK relies on an underlying BLAS implementation to pro

routines for performing common linear algebra operations

element of a basis for a function space

rotation in the plane spanned by two coordinates axes

variant of Gaussian elimination for solving tridiagonal systems of equations

numerical linear algebra algorithm

method of solving a linear system of equations

given a matrix A, the unique matrix B such that ABA = A, BAB = B, and that AB and BA are both Hermitian

eigenvalue algorithm

iterative method for computing eigenvalues and eigenvectors of a real symmetric matrix

numerical method for find eigenvalues

Mathematical algorithm

efficient and stable algorithms for finding the eigenvalues of a matrix

In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing a condition number of the problem. The preconditioned problem is then usually solved by an iterative method.

non-zero element of a matrix selected by an algorithm

algorithm to multiply matrices

frequency-domain analysis method

Binary operation, takes two matrices and returns a scalar

representation of a matrix as a sum

Algorithm for calculating determinants

iterative method for the numerical solution of a nonsymmetric system of linear equations