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Signum function = . In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether the sign of a given real number is positive or negative, or the given number is itself zero.
The sign function or signum function extracts the sign of a real number, by mapping the set of real numbers to the set of the three reals ...
The matrix sign function is a generalization of the complex signum function = {() >, <, to the matrix valued analogue ().Although the sign function is not analytic, the matrix function is well defined for all matrices that have no eigenvalue on the imaginary axis, see for example the Jordan-form-based definition (where the derivatives are all zero).
The sign, signature, or signum of a permutation σ is denoted sgn(σ) and defined as +1 if σ is even and −1 if σ is odd. The signature defines the alternating character of the symmetric group S n .
A sigmoid function is a bounded, differentiable, real function that is defined for all real input values and has a non-negative derivative at each point [1] [2] and exactly one inflection point. Properties
The Hilbert transform can be understood in terms of a pair of functions f(x) and g(x) such that the function = + is the boundary value of a holomorphic function F(z) in the upper half-plane. [32] Under these circumstances, if f and g are sufficiently integrable, then one is the Hilbert transform of the other.
A look at where the various court cases against President-elect Donald Trump stand, and how they may — or may not — be affected by his taking the oath of office on Jan. 20.
The terminology is based on what happens in the region around the value 0, and uses the analogy of viewing the input-output function of the quantizer as a stairway. Mid-tread quantizers have a zero-valued reconstruction level (corresponding to a tread of a stairway), while mid-riser quantizers have a zero-valued classification threshold ...