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  2. Matrix (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Matrix_(mathematics)

    For example, if A is a 3-by-0 matrix and B is a 0-by-3 matrix, then AB is the 3-by-3 zero matrix corresponding to the null map from a 3-dimensional space V to itself, while BA is a 0-by-0 matrix. There is no common notation for empty matrices, but most computer algebra systems allow creating and computing with them.

  3. Matrix mechanics - Wikipedia

    en.wikipedia.org/wiki/Matrix_mechanics

    Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits.

  4. Woodbury matrix identity - Wikipedia

    en.wikipedia.org/wiki/Woodbury_matrix_identity

    In mathematics, specifically linear algebra, the Woodbury matrix identity – named after Max A. Woodbury [1] [2] – says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix.

  5. Matrix analysis - Wikipedia

    en.wikipedia.org/wiki/Matrix_analysis

    In mathematics, particularly in linear algebra and applications, matrix analysis is the study of matrices and their algebraic properties. [1] Some particular topics out of many include; operations defined on matrices (such as matrix addition, matrix multiplication and operations derived from these), functions of matrices (such as matrix exponentiation and matrix logarithm, and even sines and ...

  6. Wedderburn–Artin theorem - Wikipedia

    en.wikipedia.org/wiki/Wedderburn–Artin_theorem

    In algebra, the Wedderburn–Artin theorem is a classification theorem for semisimple rings and semisimple algebras.The theorem states that an (Artinian) [a] semisimple ring R is isomorphic to a product of finitely many n i-by-n i matrix rings over division rings D i, for some integers n i, both of which are uniquely determined up to permutation of the index i.

  7. Matrix decomposition - Wikipedia

    en.wikipedia.org/wiki/Matrix_decomposition

    Download as PDF; Printable version; In other projects ... In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a ...

  8. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    The result matrix has the number of rows of the first and the number of columns of the second matrix. In mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in ...

  9. Schur decomposition - Wikipedia

    en.wikipedia.org/wiki/Schur_decomposition

    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.