Sentence examples for matrices with equal from inspiring English sources

Without any loss of generality, Eq. (5) can be rewritten as (7) The final solution for the weight components is given by (8) where * defines the Hadamard product of matrices with equal size.

From (11), we get that to achieve minimum MSE, the training signal vectors and must be designed to meet the following conditions: (1) ;   (2) and  . ; and. are two diagonal matrices with equal diagonal elements.

with a i = ∏ j = 1 M σ i, j M, where the sequence { σ i, j } j = 1 M is the singular value of H i. U1 and U2 are unitary matrices of dimensions N1 × N1 and N2 × N2, respectively, D1 and D2 are generalized upper triangular matrices with equal diagonal elements, and † denotes the conjugate transpose.

where Q i is an N i × M semi-unitary matrix, P is an M × M block diagonal matrix of the form diag (P1,P2,…,P B ), where each individual block P j is a b j × b j unitary matrix and ∑ j = 1 B b j = M. { T i } i = 1 2 are M × M upper triangular matrices with equal diagonal ratio for each block.

The implied alignment was used for statistical tests of sequence variation and other analyses requiring fixed character matrices with equal length character strings (i.e. multiple alignments).

The discretization of the Fokker Planck equation is performed using a 25-point molecule that leads to a coefficient matrix with equal number of diagonals.

It is easy to see that in (10) is a diagonal matrix with equal diagonal elements of.

In particular, if and only if all entries of are equal, then holds which is also a diagonal matrix with equal entries.

In this case, we have that A k converges, when k→∞, to a constant matrix with equal rows composed of positive elements.

The hyper-parameter matrix B is a diagonal matrix with equal entries along the diagonal, such that, where b is a positive constant.

The first method assumes a normal distribution for the pathway parameters with mean zero and diagonal variance covariance matrix with equal entries.