# matrix element

## matrix element

[′mā·triks ‚el·ə·mənt]
(mathematics)
One of the set of numbers which form a matrix.
(quantum mechanics)
The scalar product of a member of a complete, orthogonal set of vectors, representing states, with a vector which results from applying a specified operator to another member of this set.
References in periodicals archive ?
For matrix element [[rho].sub.21], the total susceptibility [chi] for the probe light is determined by
The image n with i x j pixels can be presented as a matrix with i x j elements where the location of the matrix element represents the location in the image, and the matrix element values are the grey level A(i, j,n):
Topology matrix element represents the number of hops (length of the communication path) between two nodes.
This NEON intrinsic function is used for matrix element transpose during the matrix transpose procedure in Algorithm 1.
3(b) and the coefficient matrix element in formula (1), make the link sensitivity factor [lambda] = 1, then we can get the nodes and link coefficient information.
[M.sub.jl] is the electric dipole moment off-diagonal matrix element involving those very states (in this work calculations are for circular xy-polarization of the incident radiation), whereas [[GAMMA].sub.jl] are the corresponding transition damping rates.
(1) [a.sub.pq] is matrix element; it represents a yarn carrier, p indicates the row number beginning from the bottom, p = 0, 1, 2, 3, 4, 5, 6 ...
where [V.sup.[alpha].sub.j] is the transition matrix element between the virtual state j and a scattering state [alpha] and [E.sub.j] = [[epsilon].sub.j] + [[lambda].sub.j] is the zeroth-order approximation for the resonance energy, where [[epsilon].sub.j] and [[lambda].sub.j] are single particle QD levels for temporarily trapped carriers.
Therefore, when the optimal replacement value R' = h/4 is applied to the FG-FFT, the element is regarded as the far matrix element if the nearest distance between testing function [[psi].sub.m] and basis function [[psi].sub.n] is greater than 1.75h.
Where, k is the magnetic susceptibility of adsorbed particle, [micro] is the magnetic permeability of matrix elements, [delta] is the particle size (diameter), d- is the sphere diameter of matrix element, [eta] is the dynamic viscosity of the suspension.
Thus, at any quality factor used for lossy compression of the cloned image, an indicator of the corresponding blocks of clone and prototype images [B.sub.ij] and [B.sub.kl] will be the coincident elements [g.sub.ij] = [g.sub.kl] of the matrix, in which not only the global, but also local minimum of the G can be reached (in element [g.sub.tp] the local minimum is reached if in the G matrix such neighborhood U([g.sub.tp]) exist for element [g.sub.tp], that for any matrix element [g.sub.ij] [member of] ([g.sub.tp]), [g.sub.ij] [not equal to] [g.sub.tp] the condition [g.sub.ij] > [g.sub.tp] is true).
To explain, first it is beneficial to demonstrate full O([N.sup.2.sub.b][M.sup.2.sub.b]) matrix vector product which explicitly loads each matrix element,

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