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  2. Cramer's rule - Wikipedia

    en.wikipedia.org/wiki/Cramer's_rule

    [8] [9] [verification needed] Cramer's rule can also be numerically unstable even for 2×2 systems. [10] However, Cramer's rule can be implemented with the same complexity as Gaussian elimination, [11] [12] (consistently requires twice as many arithmetic operations and has the same numerical stability when the same permutation matrices are ...

  3. Cramer's theorem (algebraic curves) - Wikipedia

    en.wikipedia.org/wiki/Cramer's_theorem_(algebraic...

    The number of distinct terms (including those with a zero coefficient) in an n-th degree equation in two variables is (n + 1)(n + 2) / 2.This is because the n-th degree terms are ,, …,, numbering n + 1 in total; the (n − 1) degree terms are ,, …,, numbering n in total; and so on through the first degree terms and , numbering 2 in total, and the single zero degree term (the constant).

  4. Cramér's theorem - Wikipedia

    en.wikipedia.org/wiki/Cramér's_theorem

    Cramér’s decomposition theorem, a statement about the sum of normal distributed random variable; Cramér's theorem (large deviations), a fundamental result in the theory of large deviations; Cramer's theorem (algebraic curves), a result regarding the necessary number of points to determine a curve

  5. Cramér's theorem (large deviations) - Wikipedia

    en.wikipedia.org/wiki/Cramér's_theorem_(large...

    The logarithmic moment generating function (which is the cumulant-generating function) of a random variable is defined as: = ⁡ ⁡ [⁡ ()].Let ,, … be a sequence of iid real random variables with finite logarithmic moment generating function, i.e. () < for all .

  6. Cramér's V - Wikipedia

    en.wikipedia.org/wiki/Cramér's_V

    In statistics, Cramér's V (sometimes referred to as Cramér's phi and denoted as φ c) is a measure of association between two nominal variables, giving a value between 0 and +1 (inclusive). It is based on Pearson's chi-squared statistic and was published by Harald Cramér in 1946.

  7. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    The equations 3x + 2y = 6 and 3x + 2y = 12 are inconsistent. A linear system is inconsistent if it has no solution, and otherwise, it is said to be consistent. [7] When the system is inconsistent, it is possible to derive a contradiction from the equations, that may always be rewritten as the statement 0 = 1. For example, the equations

  8. Leibniz formula for determinants - Wikipedia

    en.wikipedia.org/wiki/Leibniz_formula_for...

    In algebra, the Leibniz formula, named in honor of Gottfried Leibniz, expresses the determinant of a square matrix in terms of permutations of the matrix elements. If is an matrix, where is the entry in the -th row and -th column of , the formula is

  9. Cramér–Rao bound - Wikipedia

    en.wikipedia.org/wiki/Cramér–Rao_bound

    If just 2% of our most loyal readers gave $2.75 today, we'd hit our goal in a few hours. Most readers don't donate, so if Wikipedia has given you $2.75 worth of knowledge, please give. Any contribution helps, whether it's $2.75 one time or monthly.