particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily...

JSTOR 2038377. Linear Systems & Pseudo-Inverse Ben-Israel, Adi; Cohen, Dan (1966). "On Iterative Computation of Generalized Inverses and Associated Projections"...

{\Sigma }}\mathbf {c} } , its covariance with itself. Similarly, the (pseudo-)inverse covariance matrix provides an inner product ⟨ c − μ | Σ + | c − μ ⟩...

which has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can be multiplied by an inverse to undo the...

An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating...

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative...

a unit square and so a (pseudo) inverse maps the unit square to the unit interval. One way of constructing a pseudo-inverse is as follows. Let the lower-left...

Gene H.; Kahan, William (1965). "Calculating the singular values and pseudo-inverse of a matrix". Journal of the Society for Industrial and Applied Mathematics...

generalized inverse Inverse element Moore–Penrose inverse Jordan normal form Generalized eigenvector Drazin, M. P. (1958). "Pseudo-inverses in associative...

; Refregier, Ph (June 1989). "Linear and Nonlinear Extension of the Pseudo-Inverse Solution for Learning Boolean Functions". Europhysics Letters. 9 (4):...

of S. Gril p. 57 Howi p. 226 Inverse semigroup There exists unique x such that axa = a and xax = x. C&P p. 28 Left inverse semigroup (R-unipotent) Ra contains...

Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov...

decision which of the eigenvalues are close enough to zero. Pseudo-inverse The pseudo inverse of a matrix A {\displaystyle A} is the unique matrix X = A...

February 2016. Felippa, Carlos A. "Appendix D, Linear Algebra: Determinants, Inverses, Rank" (PDF). ASEN 5007: Introduction To Finite Element Methods. Boulder...

known at the transmitter, the zero-forcing precoder is given by the pseudo-inverse of the channel matrix. Zero-forcing has been used in LTE mobile networks...

x^{k+1}=x^{k}-B^{-1}A^{T}Sy^{k}} . The pseudo-inverse leads just to one particular solution. The role of the pseudo-inverse is twofold: It allows the method...

inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic...

This is accomplished through inverse transform sampling, also known as the F-Inverse method, coupled to a portable pseudo random number generator, which...

randomized algorithm F {\displaystyle F} that attempts to compute a pseudo-inverse for f succeeds with negligible probability. (The * superscript means...

modular multiplicative inverse figures prominently in the definition of the Kloosterman sum. Inversive congruential generator – a pseudo-random number generator...

Gene H.; Kahan, William (1965). "Calculating the singular values and pseudo-inverse of a matrix". Journal of the Society for Industrial and Applied Mathematics...

m is (uniformly) elliptic (of order m) and invertible, then its inverse is a pseudo-differential operator of order −m, and its symbol can be calculated...

non-bijective generators, which do not have the inverse function, the following notion of pseudo-inverse function is employed: Let f: [a, b] → [c, d] be...

= d k {\displaystyle F(e_{k})=d_{k}} . This uniquely defines the (pseudo-)inverse of F. Of course, one can choose some reconstruction formula first,...

nominal closed loop is attempted to be recovered. In the classical pseudo-inverse method, the closed loop system matrix A ¯ = A − B K {\displaystyle {\bar...

The erosion is distributive over set intersection The dilation is a pseudo-inverse of the erosion, and vice versa, in the following sense: A ⊆ ( C ⊖ B...

number of ways to deal with this. One is to use a pseudo inverse instead of the usual matrix inverse in the above formulae. However, better numeric stability...

introduced a Green's function as defined for graphs, amounting to a pseudo-inverse of the graph Laplacian.[CY00] Their work is naturally applicable to...

{\left(C^{T}C\right)^{-1}C^{T}} } is an example of a pseudo-inverse. Golub and Pereyra showed how the pseudo-inverse can be differentiated so that parameter increments...

so-called generator function and ψ − 1 {\displaystyle \psi ^{-1}} is its pseudo-inverse defined by ψ − 1 ( t ; θ ) = { ψ − 1 ( t ; θ ) if  0 ≤ t ≤ ψ ( 0 ; θ...