Sentence examples for matrices and define from inspiring English sources

In this paper, we consider Kronecker and Hadamard convolution products for matrices and define the so-called Dirac identity matrix which behaves like a group identity element under the convolution matrix operation.

By scaling, it suffices to show that when X and W are density matrices, begin{aligned} R(X||W) ge tfrac{1}{2} left| X - Wright| _1^2 end{aligned} (3.21 Let X and W be density matrices and define (H = X W W).

Example 1.1 Let A = M n ( R ) = { a = ( a i j ) n × n ∣ a i j ∈ R  for all  1 ⩽ i, j ⩽ n } be the algebra of all n-square real matrices, and define the norm ∥ a ∥ = ∑ 1 ⩽ i, j ⩽ n | a i j |.

Using suitable transformation matrices and defining a new parameter called acceleration parameter, the vertical contact forces are reformulated.

In Section 3.2, factor-specific parameters obtained by MPCA preserve the three Gram-like matrices,, and defined in (8). Figure 4 demonstrates that MPCA calculates subject, viewpoint, and lighting parameters using only the colored parts in the Gram matrix.

Corollary 4.5 Let A = ( a n k ) be an infinite matrix and define the matrix C = ( c n k ) by c n k = ∑ j = 0 n ( n j ) ( 1 − r ) n − j r j a j k ( k, n ∈ N ).

Let B the K × N beamforming matrix and define H b ≐ B H and n b ≐ B n, then the received signal becomes y b = H b s + n b. (3).

In this work, we introduce two sequence spaces c 0 λ ( G m ) and c λ ( G m ) generated by the composition of m th order generalized difference matrix and lambda matrix and define an isomorphism between new sequence spaces and classical sequence spaces.

We use the term motif to mean a set of short DNA sequences represented by a position-specific weight matrix, and define a motif match as a particular DNA sequence in a genome that is statistically similar to a motif.

This paper reviews the concept of the alias matrix, and defines the alias plot that can be obtained from the alias matrix.

This was helpful in depicting the phase distribution in the matrix and defining the causes of the residual non-wetting phase saturation.