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The Woodbury matrix identity is [5] where A, U, C and V are conformable matrices: A is n × n, C is k × k, U is n × k, and V is k × n. This can be derived using blockwise matrix inversion . While the identity is primarily used on matrices, it holds in a general ring or in an Ab-category . The Woodbury matrix identity allows cheap computation ...
Polarization identity. In linear algebra, a branch of mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. If a norm arises from an inner product then the polarization identity can be used to express this inner product entirely in ...
Milne-Thomson method for finding a holomorphic function. In mathematics, the Milne-Thomson method is a method for finding a holomorphic function whose real or imaginary part is given. [1] It is named after Louis Melville Milne-Thomson .
Subderivative. A convex function (blue) and "subtangent lines" at (red). In mathematics, subderivatives (or subgradient) generalizes the derivative to convex functions which are not necessarily differentiable. The set of subderivatives at a point is called the subdifferential at that point. [1] Subderivatives arise in convex analysis, the study ...
Conjectured in. 1939. Equivalent to. Dixmier conjecture. In mathematics, the Jacobian conjecture is a famous unsolved problem concerning polynomials in several variables. It states that if a polynomial function from an n -dimensional space to itself has Jacobian determinant which is a non-zero constant, then the function has a polynomial inverse.
In the mathematical discipline of functional analysis, a differentiable vector-valued function from Euclidean space is a differentiable function valued in a topological vector space (TVS) whose domains is a subset of some finite-dimensional Euclidean space. It is possible to generalize the notion of derivative to functions whose domain and ...
Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by , , , , or . [1]
V-statistic. V-statistics are a class of statistics named for Richard von Mises who developed their asymptotic distribution theory in a fundamental paper in 1947. [1] V-statistics are closely related to U-statistics [2] [3] (U for "unbiased") introduced by Wassily Hoeffding in 1948. [4] A V-statistic is a statistical function (of a sample ...