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Also, positive semidefiniteness, combined with another necessary condition, consistency, is a sufficient condition in the case of extremal moment problems, i.e., when the rank of the moment matrix (denoted by r) and the cardinality of the associated algebraic variety (denoted by v) are equal.
Stack these three matrices in a I+J+K by R matrix denoted by X.
Consider a MIMO channel with transmit antennas and receive antennas, with the link gain matrix denoted by a real matrix.
More precisely, given a realization of an observation vector, we obtain the square root of the covariance matrix, denoted by.
The -mode product of a tensor by a matrix, denoted by, is a tensor with entries [30 32]: (1).
A weighted mean matrix, denoted by, is a lower triangular matrix with entries, where is a nonnegative sequence with, and.
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Based on the above results, we can construct the three two-dimensional matrices, denoted by D Y, D U, and D V, respectively, with the same size as the corresponding components, i.e., Y, U, and V components.
Let the region be covered by p SNPs genotyped in both samples, with the genotype matrices denoted by X = X 1,..., X p and X ′ = X 1 ′,..., X p ′, respectively.
The filtered and normalized double-mutant fitness data matrix, denoted here by WSGA, was treated as the input of our computational data transformation pipeline (see Figure 5).
An M×M identity matrix is denoted by I M. The Frobenius norm of a matrix is denoted by ∥·∥F.
If is a matrix, denote by its operator norm, that is,, where (resp., ) means the largest (resp., smallest) eigenvalue of.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com