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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 ...
Though Cramer's rule is important theoretically, it has little practical value for large matrices, since the computation of large determinants is somewhat cumbersome. (Indeed, large determinants are most easily computed using row reduction.)
Cramer's rule on the other hand needs to make no decisions at all (all that matters is that the denominator is nonzero, which is the condition for a unique solution to exist in the first place) and can be applied to such a system. That is exactly why the rule is of theoretical importance.
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).
The Cramér–Rao bound is stated in this section for several increasingly general cases, beginning with the case in which the parameter is a scalar and its estimator is unbiased.
Cramér's theorem may refer to . 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
In mathematics, the Cramér–Wold theorem [1] [2] or the Cramér–Wold device [3] [4] is a theorem in measure theory and which states that a Borel probability measure on is uniquely determined by the totality of its one-dimensional projections.
The Möller–Trumbore ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle. [1]