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2. 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.

3. Mathematics - Wikipedia

   en.wikipedia.org/wiki/Mathematics

   Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements. [4] Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions ), until the 16th and 17th centuries, when algebra [ a ...

4. 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]).

5. Lebesgue's decomposition theorem - Wikipedia

   en.wikipedia.org/wiki/Lebesgue's_decomposition...

   Lebesgue's decomposition theorem can be refined in a number of ways. First, as the Lebesgue-Radon-Nikodym theorem. That is, let (,) be a measure space, a σ-finite positive measure on and a complex measure on . [4]

6. Eigendecomposition of a matrix - Wikipedia

   en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix

   The decomposition can be derived from the fundamental property of eigenvectors: = = =. The linearly independent eigenvectors q i with nonzero eigenvalues form a basis (not necessarily orthonormal) for all possible products Ax, for x ∈ C n, which is the same as the image (or range) of the corresponding matrix transformation, and also the ...

7. NYT ‘Connections’ Hints and Answers Today, Wednesday, January 8

   www.aol.com/nyt-connections-hints-answers-today...

   4. These words are related to a particular genre of music (hint: they deal with "names" that are spelled a little differently). Related: 300 Trivia Questions and Answers to Jumpstart Your Fun Game ...