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  2. Cramer's rule - Wikipedia

    en.wikipedia.org/wiki/Cramer's_rule

    Cramer's rule, implemented in a naive way, is computationally inefficient for systems of more than two or three equations. [7] In the case of n equations in n unknowns, it requires computation of n + 1 determinants, while Gaussian elimination produces the result with the same computational complexity as the computation of a single determinant.

  3. Manin matrix - Wikipedia

    en.wikipedia.org/wiki/Manin_matrix

    Cramer's rule (See [2] or section 4.1. [3]) The inverse to a Manin matrix M can be defined by the standard formula: M − 1 = 1 det c o l ( M ) M a d j , {\displaystyle M^{-1}={\frac {1}{{\det }^{col}(M)}}M^{adj},} where M adj is adjugate matrix given by the standard formula - its (i,j)-th element is the column-determinant of the (n − 1) × ...

  4. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    Cramer's rule is a closed-form expression, in terms of determinants, of the solution of a system of n linear equations in n unknowns. Cramer's rule is useful for reasoning about the solution, but, except for n = 2 or 3, it is rarely used for computing a solution, since Gaussian elimination is a faster algorithm.

  5. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    A linear system in three variables determines a collection of planes. The intersection point is the solution. In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. [1] [2] For example,

  6. 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).

  7. Cramér–Rao bound - Wikipedia

    en.wikipedia.org/wiki/Cramér–Rao_bound

    The result is named in honor of Harald Cramér and Calyampudi Radhakrishna Rao, [1] [2] [3] but has also been derived independently by Maurice Fréchet, [4] Georges Darmois, [5] and by Alexander Aitken and Harold Silverstone. [6] [7] It is also known as Fréchet-Cramér–Rao or Fréchet-Darmois-Cramér-Rao lower bound.

  8. Glossary of calculus - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_calculus

    Examples of proper fractions are 2/3, –3/4, and 4/9; examples of improper fractions are 9/4, –4/3, and 3/3. improper integral In mathematical analysis , an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number , ∞ {\displaystyle \infty } , − ∞ ...

  9. 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