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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 ...
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 ...
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.
The term 1. /. ρ2∇ρ × ∇p is the baroclinic term. It accounts for the changes in the vorticity due to the intersection of density and pressure surfaces. The term ∇ × ( ∇ ∙ τ. /. ρ), accounts for the diffusion of vorticity due to the viscous effects. The term ∇ × B provides for changes due to external body forces.
Generation Z (often shortened to Gen Z ), colloquially known as Zoomers, [1] [2] [3] is the demographic cohort succeeding Millennials and preceding Generation Alpha. Researchers and popular media use the mid-to-late 1990s as starting birth years and the early 2010s as ending birth years.
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 ...