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ScaLAPACK is a library of high-performance linear algebra routines for parallel distributed-memory machines that features functionality similar to LAPACK (solvers for dense and banded linear systems, least-squares problems, eigenvalue problems, and singular-value problem). Scilab is advanced numerical analysis package similar to MATLAB or Octave.
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a rescaling followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any m × n {\displaystyle m\times n} matrix.
He developed MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor, George Forsythe. [21] This was followed by Fortran code for linear equations in 1971. [21] Before version 1.0, MATLAB "was not a programming language; it was a simple interactive matrix calculator. There were no programs, no toolboxes, no graphics.
In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary complex square matrix as unitarily similar to an upper triangular matrix whose diagonal elements are the eigenvalues of the original matrix.
In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix multiplication and matrix decomposition). The product sometimes includes a permutation matrix as well.
where R 1 is an n×n upper triangular matrix, 0 is an (m − n)×n zero matrix, Q 1 is m×n, Q 2 is m×(m − n), and Q 1 and Q 2 both have orthogonal columns. Golub & Van Loan (1996 , §5.2) call Q 1 R 1 the thin QR factorization of A ; Trefethen and Bau call this the reduced QR factorization . [ 1 ]
Also a computer algebra system through interface with Maxima: Fityk: Marcin Wojdyr 2002 1.3.1 19 December 2016: $115 (1.x binaries), Free (source code and 0.x binaries) GPL: interactive graphics, scriptable, specialized in curve fitting and peak fitting, 2D only FlexPro: Weisang GmbH n/a 1991 2019 (12.0.x) 2018 Not free (commercial), Free ...
In linear algebra, the identity matrix of size is the square matrix with ones on the main diagonal and zeros elsewhere. It has unique properties, for example when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous to multiplying by the number 1.