Sentence examples for matrix given as from inspiring English sources

where is the CP removal matrix given as (9).

where, (19). is obtained by the identity matrix by reversing the column order, and is a permutation matrix given as.

The vector is the CFO vector containing the CFO values from all users, and the channels of all users are stacked into the channel matrix given as (5).

where Z is the K×K matrix given as begin{array}rcl@ Z= left[begin{array}{cccc} 0 & & & vdots & & I_{K-1} & 0 & & & D & 0 & cdots & 0 end{array}right] end{array} (7).

Therefore, by integrating the steering vector correlation, we can build a positive definite matrix given as follows {mathbf{P}}_a={displaystyle underset{varTheta }{int }{mathbf{s}}_aleft(theta right){mathbf{s}}_a^Hleft(theta right)dtheta } (11).

Case a: If N=2, the optimal F D,i is a diagonal matrix given as begin{array}rcl@ mathbf{F}_{D,i} &triangleq& { left[begin{array}{cc} mathbf{f}_{d,i,1} & mathbf{0} mathbf{0} & mathbf{f}_{d,i,2} end{array}right]}.

Then, there are L square rank one matrices given as A1, A2,..., A L, such that A = A1 + A2 +... + A L and an alternative proof can be derived for such matrices.

α →, β Open image in new window are the 4 × 4. Dirac matrices given as α → = 0 σ → i σ → i 0, β = I 0 0 - I, Open image in new window (20).

The variance of the elements of the channel matrix is given as, where is the distance between BS and user, is the path loss exponent, and is a zero mean Gaussian random variable with variance, modeling the lognormal shadowing.

As in other energies mentioned in the above paragraph, we can define a new energy by considering the Kirchhoff matrix given in (2) as follows.

The Independent model Q matrix or substitution rate matrix is given as: Where g i is the genotype state and p i is the phenotype state at point i.