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  2. List of open-source software for mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_open-source...

    It was originally known as "HECKE and Manin". After a short while it was renamed SAGE, which stands for ‘’Software of Algebra and Geometry Experimentation’’. Sage 0.1 was released in 2005 and almost a year later Sage 1.0 was released. It already consisted of Pari, GAP, Singular and Maxima with an interface that rivals that of Mathematica.

  3. Schur decomposition - Wikipedia

    en.wikipedia.org/wiki/Schur_decomposition

    There is also a real Schur decomposition. If A is an n × n square matrix with real entries, then A can be expressed as [4] = where Q is an orthogonal matrix and H is either upper or lower quasi-triangular. A quasi-triangular matrix is a matrix that when expressed as a block matrix of 2 × 2 and 1 × 1 blocks is

  4. MATLAB - Wikipedia

    en.wikipedia.org/wiki/MATLAB

    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.

  5. List of numerical-analysis software - Wikipedia

    en.wikipedia.org/wiki/List_of_numerical-analysis...

    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.

  6. Square matrix - Wikipedia

    en.wikipedia.org/wiki/Square_matrix

    For instance, the main diagonal of the 4×4 matrix above contains the elements a 11 = 9, a 22 = 11, a 33 = 4, a 44 = 10. In mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order . Any two square matrices of the same order can be added and multiplied.

  7. Schur's theorem - Wikipedia

    en.wikipedia.org/wiki/Schur's_theorem

    As a result, for every set of relatively prime numbers {, …,} there exists a value of such that every larger number is representable as a linear combination of {, …,} in at least one way. This consequence of the theorem can be recast in a familiar context considering the problem of changing an amount using a set of coins.

  8. Computational mathematics - Wikipedia

    en.wikipedia.org/wiki/Computational_mathematics

    The tablet also gives an example where one side of the square is 30, and the resulting diagonal is 42 25 35 or 42.4263888. Computational mathematics is the study of the interaction between mathematics and calculations done by a computer.

  9. Cramer's rule - Wikipedia

    en.wikipedia.org/wiki/Cramer's_rule

    In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the ...