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  2. List of numerical-analysis software - Wikipedia

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

    [1] [2] [3] It comes with its own programming language, in which numerical algorithms can be implemented. GNU MCSim a simulation and numerical integration package, with fast Monte Carlo and Markov chain Monte Carlo capabilities. ML.NET is a free-software machine-learning library for the C# programming language. [4] [5]

  3. QR decomposition - Wikipedia

    en.wikipedia.org/wiki/QR_decomposition

    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 ]

  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. 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

  6. Identity matrix - Wikipedia

    en.wikipedia.org/wiki/Identity_matrix

    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.

  7. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    Functional analysis applies the methods of linear algebra alongside those of mathematical analysis to study various function spaces; the central objects of study in functional analysis are L p spaces, which are Banach spaces, and especially the L 2 space of square-integrable functions, which is the only Hilbert space among them. Functional ...

  8. Square matrix - Wikipedia

    en.wikipedia.org/wiki/Square_matrix

    A square matrix of order 4. The entries form the main diagonal of a 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.

  9. Math Kernel Library - Wikipedia

    en.wikipedia.org/wiki/Math_Kernel_Library

    Linear algebra: BLAS routines are vector-vector (Level 1), matrix-vector (Level 2) and matrix-matrix (Level 3) operations for real and complex single and double precision data. LAPACK consists of tuned LU, Cholesky and QR factorizations, eigenvalue and least squares solvers.