Sentence examples for becomes a diagonal matrix from inspiring English sources

If the components of X are independent from each other, then, Υ becomes a diagonal matrix.

In the case that each supporting limb only supplies one driving force/torque or constraint force/moment, the stiffness of each limb is just a scalar quantity, and the weighted matrix B becomes a diagonal matrix, which is consistent with the work done in Refs. [53, 54].

In that case, equation (3) becomes (4) With, a diagonal matrix with elements with being the phenotypic variance, heritability h, and repeatability t.

For a system consisting of independent subsystems, the columns and rows of M can be permuted such that it becomes a block diagonal matrix with each block corresponding to its own subsystem.

From Equation (39) it becomes clear that Ψ must be a diagonal matrix.

Consider a larger between-study variance, so that Σ becomes Σ M and Σ 1/2 becomes Σ 1/2 M 1/2, where M is a diagonal matrix in which all diagonal entries and hence all eigenvalues are also greater than one.

For this study, we assumed that the two terms, the trend and the seasonal variation, were independent, and hence, W became a block diagonal matrix.

Here exp(θ D) becomes simple componentwise exponentiation because D is a diagonal matrix of eigenvalues.

We can easily derive the gradient and the Hessian results in a diagonal matrix whose inversion using Newton's method then becomes a point-wise division.

In case of a time-invariant channel, the channel matrix H ~ n t, n r appears as a diagonal matrix, whereas a time-variant channel forces the channel matrix H ~ n t, n r to become non-diagonal.

where, is a transpose operation, is an diagonal matrix with the as its main diagonal.