Sentence examples for matrices with mean from inspiring English sources

Let us suppose that (phantom {dot {i}!}E_{i}=(boldsymbol {varepsilon }_{i1},boldsymbol {varepsilon }_{i2},ldots,boldsymbol {varepsilon }_{iK})= varepsilon _{ij_{im}k})_{m=1,2,ldots,M k=1,2,ldots,K}) are independent random matrices with mean E[E i ]=0 M 0 K′ and covariance V[vec(E i )]=Σ⊗Ξ, where Σ and Ξ are an unknown (K×K -dimensional matrix and a K×K -dimensionalnsional matrix, respectively.

MVN n  ×  d (0,  V1,  V2) denotes the n ×  d matrix normal distribution with mean 0, row covariance matrix V1 (n by n) and column covariance matrix V2 (d by d).

It follows then the channel matrix  H can be expressed as H = H ^ + E, where H ^ is the predicted channel matrix with zero mean and variance ( 1 - ψ ) and  E is the CSI error matrix with zero mean and mean square error  ψ.

In fact, GRMM is a complex Gaussian random matrix with zero mean and covariance matrix I.

Annealing at 400 °C results in crystalline anatase TiO2 matrix with its mean crystallite size decreasing with increasing the [Au]/[Ti] ratio in the composite layers.

Nanocrystallites of a body-centered cubic ferritic solid solution matrix with a mean size of approximately 20 nm were observed by transmission electron microscopy.

Correlation matrices are symmetric, and for simplicity, we denote H ̄ mi = R r 1 2 H ̄ i R i 1 2 and E mi = R r 1 2 E i T I N + σ i 2 R i − 1 − T 2, where these represent each channel matrix with a mean part and an estimation error part.

A sub-matrix with a mean squared residue score below a chosen threshold is termed a δ-bicluster.

The multivariate linear regression model takes the form where B*∈ ℝ d× k is the regression coefficients matrix and ∈ ∈ℝ n× k is the noise matrix with zero mean.

The pi statistic is calculated as the deviation of the actual resemblance profile of the resemblance matrix with the mean profile.

The smallest entries in the matrix of β-weights were pruned until the non-zero entries of the matrix represented a graph with mean degree, d, where different values of d were used in different cases.