Sentence examples for matrix notation for from inspiring English sources

If channel state information (CSI) is known for receiver, the channel capacity of the MIMO-NB system can be written in an equivalent matrix notation for N t  ≥ N r as follows [34 36]: C NB = B log 2 det I + SNR t N t H H *, (6).

It is well known that the eigenvalues of the adjoint equation corresponding to (B.1) are same as that of (B.1) but eigenfunctions are given by ( − θ 2 ϕ − l, θ 1 ϕ − l ) for − l ∈ N and ( θ 2 ϕ l, θ 1 ϕ l ) for l ∈ N. Using matrix notation for convenience, the eigenvalue problem (B.1) reads as follows: − Δ [ w 1 w 2 ] = λ a ( x ) [ 0 θ 1 θ 2 0 ] [ w 1 w 2 ] in  Ω.

While in the main text, tensors are denoted as bold face symbols, in the supplement we often use an explicit index or matrix notation for tensors.

In matrix notation, for each trait the model is specified as follows: (3) where y is the vector of phenotypic observations for all individuals, μ is the mean phenotype, and b is the vector of fixed effects to be fitted (age) and X the design matrix relating phenotypic observations to the vector of fixed effects.

For the sake of simplicity, we use matrix notation H for all fading scenarios considered in this paper.

In brief, the matrix-notation for propagation of the electric fields as presented in the present study allows the influence of tight focusing to be incorporated through multiplication by an additional "local field" matrix.

In 1857, Cayley introduced the matrix notation which allows for a harmonization and simplification of linear maps.

For simplicity, matrix notation has been used, and sex, region and country indexes have not been shown explicitly.

For simplicity the subscript will be dropped from the J matrix notation.

Matrix notation is employed.

Especially for higher space dimensions, it is claimed that a band tensor formulation better corresponds to the inherent problem structure than does conventional matrix notation.