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Cramer's rule. 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 ...
In algebraic geometry, Cramer's theorem on algebraic curves gives the necessary and sufficient number of points in the real plane falling on an algebraic curve to uniquely determine the curve in non- degenerate cases. This number is. where n is the degree of the curve. The theorem is due to Gabriel Cramer, who published it in 1750.
Cramér–Rao bound. Illustration of the Cramer-Rao bound: there is no unbiased estimator which is able to estimate the (2-dimensional) parameter with less variance than the Cramer-Rao bound, illustrated as standard deviation ellipse. In estimation theory and statistics, the Cramér–Rao bound (CRB) relates to estimation of a deterministic ...
The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. [1][2][3] Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental ...
February 1698 – 14 June 1746) [1] was a Scottish mathematician who made important contributions to geometry and algebra. [2] He is also known for being a child prodigy and holding the record for being the youngest professor. The Maclaurin series, a special case of the Taylor series, is named after him.
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, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously ...
In linear algebra, the adjugate or classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. [1] [2] It is occasionally known as adjunct matrix, [3] [4] or "adjoint", [5] though that normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose.
Intersection problems between a line and a conic section (circle, ellipse, parabola, etc.) or a quadric (sphere, cylinder, hyperboloid, etc.) lead to quadratic equations that can be easily solved. Intersections between quadrics lead to quartic equations that can be solved algebraically.