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In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the ...
A linear system in three variables determines a collection of planes. The intersection point is the solution. ... Cramer's rule is an explicit formula for the ...
It may be viewed as the association between two variables as a percentage of their maximum possible variation. φ c 2 is the mean square canonical correlation between the variables. [citation needed] In the case of a 2 × 2 contingency table Cramér's V is equal to the absolute value of Phi coefficient.
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
Consistency and independence of the equations in the set is established because the determinant of coefficients is non-zero, so a solution can be found using Cramer's rule. Using the examples from the subsection Elements of signal-flow graphs, we construct the graph In the figure, a signal-flow graph in this case.
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).
Comparative statics results are usually derived by using the implicit function theorem to calculate a linear approximation to the system of equations that defines the equilibrium, under the assumption that the equilibrium is stable.
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 .