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  2. Matrix (mathematics) - Wikipedia

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

    Others, such as matrix addition, scalar multiplication, matrix multiplication, and row operations involve operations on matrix entries and therefore require that matrix entries are numbers or belong to a field or a ring. [8] In this section, it is supposed that matrix entries belong to a fixed ring, which is typically a field of numbers.

  3. 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 ...

  4. Outline of linear algebra - Wikipedia

    en.wikipedia.org/wiki/Outline_of_linear_algebra

    This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices. Linear equations

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    The AOL.com video experience serves up the best video content from AOL and around the web, curating informative and entertaining snackable videos.

  6. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    Matrix multiplication is defined in such a way that the product of two matrices is the matrix of the composition of the corresponding linear maps, and the product of a matrix and a column matrix is the column matrix representing the result of applying the represented linear map to the represented vector. It follows that the theory of finite ...

  7. Row and column vectors - Wikipedia

    en.wikipedia.org/wiki/Row_and_column_vectors

    In linear algebra, a column vector with ⁠ ⁠ elements is an matrix [1] consisting of a single column of ⁠ ⁠ entries, for example, = [].. Similarly, a row vector is a matrix for some ⁠ ⁠, consisting of a single row of ⁠ ⁠ entries, = […]. (Throughout this article, boldface is used for both row and column vectors.)

  8. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    For some sparse matrices, the introduction of randomness improves the speed of the iterative methods. [10] One example of an iterative method is the Jacobi method , where the matrix A {\displaystyle A} is split into its diagonal component D {\displaystyle D} and its non-diagonal component L + U {\displaystyle L+U} .

  9. Elementary matrix - Wikipedia

    en.wikipedia.org/wiki/Elementary_matrix

    In mathematics, an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix. The elementary matrices generate the general linear group GL n ( F ) when F is a field .

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