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  2. Rouché–Capelli theorem - Wikipedia

    en.wikipedia.org/wiki/Rouché–Capelli_theorem

    Consider the system of equations x + y + 2z = 3, x + y + z = 1, 2x + 2y + 2z = 2.. The coefficient matrix is = [], and the augmented matrix is (|) = [].Since both of these have the same rank, namely 2, there exists at least one solution; and since their rank is less than the number of unknowns, the latter being 3, there are infinitely many solutions.

  3. Equation xy = yx - Wikipedia

    en.wikipedia.org/wiki/Equation_xy_=_yx

    "x^y = y^x - commuting powers". Arithmetical and Analytical Puzzles. Torsten Sillke. Archived from the original on 2015-12-28. dborkovitz (2012-01-29). "Parametric Graph of x^y=y^x". GeoGebra. OEIS sequence A073084 (Decimal expansion of −x, where x is the negative solution to the equation 2^x = x^2)

  4. Noisy-channel coding theorem - Wikipedia

    en.wikipedia.org/wiki/Noisy-channel_coding_theorem

    Graph showing the proportion of a channel’s capacity (y-axis) that can be used for payload based on how noisy the channel is (probability of bit flips; x-axis) The basic mathematical model for a communication system is the following:

  5. XY problem - Wikipedia

    en.wikipedia.org/wiki/XY_problem

    The XY problem is a communication problem encountered in help desk, technical support, software engineering, or customer service situations where the question is about an end user's attempted solution (X) rather than the root problem itself (Y or Why?). [1]

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    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  7. Big O notation - Wikipedia

    en.wikipedia.org/wiki/Big_O_notation

    Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by German mathematicians Paul Bachmann, [1] Edmund Landau, [2] and others, collectively called Bachmann–Landau notation or asymptotic notation.

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  9. Functor represented by a scheme - Wikipedia

    en.wikipedia.org/wiki/Functor_represented_by_a...

    Hom(−,X) : (Affine schemes) op Sets. sending an affine scheme Y to the set of scheme maps. [4] A scheme is determined up to isomorphism by its functor of points. This is a stronger version of the Yoneda lemma, which says that a X is determined by the map Hom(−,X) : Schemes op → Sets.