Sentence examples for matrix defined above from inspiring English sources

S is the stoichiometric matrix defined above.

2. Dissimilarity matrix D = { d ij } i, j  = 1 N  = 1 N 1 N T  −  K, where K is a similarity matrix defined above.

The mixing matrix e is then just (20) Noting that Tr FF T = S, the modularity matrix defined above (8), we find that (21) The same construction also allows us to write Q H [defined in Eq. (11)] in terms of Tr e [Eq. (12)] by noting that (22) where 1 is a matrix where each entry is 1.

For the prior covariance Σ V of maximum reaction rates, we take a unit information formulation of the truncated g-prior, so that p (V | K, σ ) = N T (V ; μ V, n σ 2 (D ′ D ) − 1 ) where D = D G, S (K ) is the design matrix defined above.

However, as we show in section 1 of Additional file 1 the values in Eq. (14) can be calculated faster if we precompute either and, or and depending on which pair of matrices is fastest to compute, where I is the d v × d v' matrix defined above.

Exponential correlation matrices defined above have full rank.

The sequence ({H_{k}}) of matrices defined above possesses nice properties as follows.

Like the other vectors and matrices defined above, these four entities can be further decomposed into their left and right subsets, labeled with the indices and, respectively.

where denotes the matrix defined by.

Afterwards, we also formulate the eigenvalues and determinant of the matrix H defined above.

Our ultimate goal would be to use this expression to directly conclude that the number of necessary measurements m in the QNC scenario is of the same order as that of a well-known Gaussian measurement matrix, as defined above.