Sentence examples for reduced matrix equation from inspiring English sources

Finally, the dimension reduced matrix equation of the inverse problem is formed by assembling the dimension reduced sub matrix equations of all the projections as follows (16) Γ t = Ξ t X, where Γ t = { Γ s t } and Ξ t = { Ξ s t }.

After retaining the first t large principal components and leaving out the rest less significant principal components of Ξ s and Γ s, a dimension reduced sub matrix equation is given as follows (14) Γ s t = Ξ s t X.

It is also shown that the conditions are constructive and can be reduced to an algebraic Lyapunov matrix equation by which nonlinear feedback in the observer and its corresponding Lyapunov function can be searched in a way parallel to those of nonlinear control design.

For markers transmitted only through females, the selection matrix (Equation B1) reduces to S ˜ = S 1 ⊗ … S l, with S i containing only the female selection parameter σf, i, and the recombination matrix R ˜ = R 1 ⊗ … R l contains the crossover rates for females alone.

The domain decomposition method was used to divide physical domain of the problem into sub-domains and obtain a reduced form of the global stiffness matrix equation.

It is easy to see that matrix equation (1) can be reduced to X + A ⋆ X − 1 A + B ⋆ X − 1 B = I, (2).

This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method.

Based on the parametric solutions of a Sylvester matrix equation, a parametric expression for all the gain matrices of reduced-order state observers is presented, and a parametric design method of reduced-order state observers is proposed.

Let the matrix equation (2.8).

Matrix equation can be constructed as: (5).

leads to the matrix equation (10).