Sentence examples for matrix with components from inspiring English sources

Define the matrix with components.

We note that the Jacobian has the form of a graph-Laplacian mixing both anatomy and dynamics, namely it is the graph-Laplacian of the matrix with components (-w_{ij}H' varphi_{j}-varphi_{i})).

For Open image in new window, the matrix a s,S s)) has to be replaced by the matrix with components a ij (s,S s))S i (s S j (s).

The initial state (x 0)) is Gaussian with state (rho_{0}) and satisfies the commutation relations1 bigl[x_{j}(0),x_{k}(0 bigr]=2iTheta_{jk},quad j,k=1,2,ldots,n, where Θ is a real antisymmetric matrix with components (Theta _{jk}) and (i=sqrt{-1}).

For Open image in new window, the matrix a s,S s)) needs to be replaced by the matrix with components a ij (s,S s))S i (s S j (s), and we arrive at (2.9) by the same arguments as in the case of Open image in new window.

We introduce the N × N matrix with components: (9) where H′ = dH/ dθ.

We can convert the covariance matrix, Σ0 to correlation matrix Σ with components r ij = σ ij σ ii σ jj.

Here, "diag(E)" indicates the diagonal 3×3 matrix with the components of E along the diagonal.

When the number of objects is large, a part of the objects is often assigned randomly to each evaluator, and the response becomes a matrix with missing components.

Let   be an positive definite Hermitian matrix and its eigenvalues, let be the diagonal matrix with the components of as its diagonal elements, and also let Then for some unitary matrix (where is the conjugate transpose of and see [9, 13]).

Thus, one may alternatively consider the effect of J out, the Jones matrix that transforms E out to I z s), as the product of a scaling matrix (with real components) and a rotation matrix (with unit norm).