Sentence examples for by applying the matrix from inspiring English sources

Note that (28) is obtained from (27) by applying the matrix inversion lemma, and using the fact that.

By applying the matrix decomposition, we get ({hat {mathbf {Q}}}_{mathbf {v}}=hat {mathbf {v}}{hat {mathbf {v}}}^{H}).

These three values are used as output values by applying the matrix related to the weights ((a_{i,j})) in Eq. (3).

Specifically, by applying the matrix inversion lemma to the 2×2 block matrix B−1 with diagonal blocks, it can be shown that the trace in (54) is applied on a sum of diagonal matrices.

and finally by applying the matrix inversion lemma lambda_{{mathbf{K}}}=beta_{infty} left[2Lambda_{mathrm{u}}-mu m_{mathrm{f}}^{(2,2 }Lambda_{mathrm{u}}^{2}right]^{-1}lambda_{mathrm{u}}.

By applying the matrix inversion lemma to the MMSE solution of Equation (16) and considering afterwards the limiting case when ξ t → 0, the expressions for the ZF linear precoder can be readily obtained and expressed as follows F ZF = g ZF - 1 H H H H H H ) - 1, g ZF = tr H H H 1 1 C u E tx. (17).

Such a tedious task can be turned into a breeze by repeatedly applying the matrix identities [29] ( I + U ) − 1 = I − U ( I + U ) − 1, V ( I + U V ) − 1 = ( I + V U ) − 1 V. (14).

Moreover, the time-dependent stability conditions are derived by applying the linear matrix inequality (LMI).

The first example shows the identification of the significant patterns of fracture intensity categories by applying the probability matrix.

The analytic expressions of the transmission amplitude and conductance are derived by applying the transfer matrix method in the one-electron scattering formalism.

The linear and non-linear (large amplitude), axisymmetric free vibration of a circular plate of variable thickness, with immovable edges, is analyzed by applying the transfer matrix method.