Sentence examples for using the diagonal matrix from inspiring English sources

A new image A 1 is generated using the diagonal matrix B 1 and the two orthogonal matrices.

The scaling operations (19 - 20) can be written using the diagonal matrix ( mathbf{D}=left[{d}_nright]in {mathcal{R}}^ ), where ( {d}_nkern0.3em =kern0.3em 1/sQ}t{{left[{mathbf{Q}_2^{astt }{mathbf{Q}}_2right]}_{nn}} ) and nn denotes the nth diagonal element.

We also use the diagonal matrix (C_{d}) which has the same elements on the diagonal as C. Let there exist a neighborhood ({mathcal{O}}(o)), in which the function delta(x) = 2x^{T} C f(x) + h^{T}(x) C_{d} h(x) (6) is negative definite with respect to system (3).

This is a centroid distance based approach as well, but neglects inter-correlation of feature values (by computing the distance using the diagonal elements of the hat matrix).

As is observed in Fig. 6a, b, by using the diagonal block structure of the connectivity matrix or the cluster crossing curve, the boundaries between classes can be delineated.

The confidence intervals for the values of the fitting parameters were calculated using the diagonal elements of the inverted Hessian matrix, as described by Hamilton (37).

From this definition, w y d can be expressed as: mathop wnolimits_{y}^{d} = hat{eta } cdot y (21 where (mathop eta limits^{ wedge }) is the diagonal matrix of direct water use coefficients and y is the column vector of final demand.

The diagonal matrix (after decomposition on SVD) S is used for inserting the watermark after decomposition on wavelet transform.

What is the rank of the diagonal matrix below?

where denotes the diagonal matrix.

denotes the diagonal matrix with diagonal elements the elements of.