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  2. Decomposition of a module - Wikipedia

    en.wikipedia.org/wiki/Decomposition_of_a_module

    A decomposition with local endomorphism rings [5] (cf. #Azumaya's theorem): a direct sum of modules whose endomorphism rings are local rings (a ring is local if for each element x, either x or 1 − x is a unit). Serial decomposition: a direct sum of uniserial modules (a module is uniserial if the lattice of submodules is a finite chain [6]).

  3. Partial fraction decomposition - Wikipedia

    en.wikipedia.org/wiki/Partial_fraction_decomposition

    In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

  4. Polynomial decomposition - Wikipedia

    en.wikipedia.org/wiki/Polynomial_decomposition

    In mathematics, a polynomial decomposition expresses a polynomial f as the functional composition of polynomials g and h, where g and h have degree greater than 1; it is an algebraic functional decomposition. Algorithms are known for decomposing univariate polynomials in polynomial time.

  5. Mathematical visualization - Wikipedia

    en.wikipedia.org/wiki/Mathematical_visualization

    The Mandelbrot set, one of the most famous examples of mathematical visualization.. Mathematical phenomena can be understood and explored via visualization.Classically, this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century).

  6. Primary decomposition - Wikipedia

    en.wikipedia.org/wiki/Primary_decomposition

    The components of a primary decomposition (as well as of the algebraic set decomposition) corresponding to minimal primes are said isolated, and the others are said embedded. For the decomposition of algebraic varieties, only the minimal primes are interesting, but in intersection theory , and, more generally in scheme theory , the complete ...

  7. Matrix decomposition - Wikipedia

    en.wikipedia.org/wiki/Matrix_decomposition

    Decomposition: This is a version of Schur decomposition where and only contain real numbers. One can always write A = V S V T {\displaystyle A=VSV^{\mathsf {T}}} where V is a real orthogonal matrix , V T {\displaystyle V^{\mathsf {T}}} is the transpose of V , and S is a block upper triangular matrix called the real Schur form .

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