where Φ is the optimized code matrix and denotes a matrix with values whose elements approach 0. By substituting (9) into (57), we can rewrite (57) as (58).
denotes expectation, denotes the trace of a matrix, denotes the th entry of a vector.
denotes the trace of a matrix, denotes the identity matrix of order, denotes the logarithm of base 2, represents the expectation operator, and the superscript denotes hermitian transposition operation.
The term-document matrix, denoted as A, plays a central role in our analysis (see Manning et al. 2008).
Superscript 'T' denotes the transposition of a vector or a matrix; ⋆ represents the elements below the main diagonal of a symmetric block matrix; I denotes an identity matrix; '-' in tables represents no feasible solution for matrix inequality.
The -mode product of a tensor by a matrix, denoted by, is a tensor with entries [30 32]: (1).
Consider a MIMO channel with transmit antennas and receive antennas, with the link gain matrix denoted by a real matrix.
Note that the path-arc incidence matrix and the path-O/D pair incidence matrix, denoted by A and B, respectively, are determined by the given network and O/D pairs.
In notation, matrix T denotes an n by t matrix of transcript data, where the element in the ith row and jth column is the expression level of the jth transcript of the ith individual.
A weighted mean matrix, denoted by, is a lower triangular matrix with entries, where is a nonnegative sequence with, and.
