Sentence examples for matrix equations in from inspiring English sources

Using simple matrix equations, in this commentary I demonstrate that the end result of a Bass Ackwards analysis that is, the correlations between component scores from different levels of a hierarchy can be calculated without calculating the actual component scores.

Because of the principal applications of generalized inverses is to the solution of linear systems and matrix equations in the singular case, we use the generalized inverse of matrices to demonstration that the transform function of the neural synaptic matrix is trapdoor one-way function.

Thus to characterize (1.3) is in fact to solve the four matrix equations in (1.4 - 1.7 1.4 - 1.7

The homogeneous and the inhomogeneous integral equations can then be written as matrix equations in the covariants and the discretized momenta and read (12) F [ h ] i, P = K j, Q i, P F [ h ] j, Q in the homogeneous case, and (13) F i, P = F 0 i, P + K j, Q i, P F j, Q in the inhomogeneous case.

In a first step, the WMT is used to get a sparse matrix equation in wavelet-domain.

Closed form solutions to a family of generalized Sylvester matrix equation in form of ∑i="0ϕAiXFi+∑i="0ψBkYFk="∑j="0φEjRFj are given by using the so-called Kronecker matrix polynomials.

Similarly to previous work on this method, the resulting matrix equation in the present approach is solved using a block-LU decomposition.

The well-known Singular Value Decomposition solution technique, which is adopted here for the solution of the system matrix equation in its complex form, is briefly outlined.

In this article,first of all, we are to solve the following matrix equation in different cases and try to generalize the result for greater dimensions: X X ¯ = a b c d = A. Open image in new window (2).

These parameters are used to calculate GIC (I, in ampere) along power transmission lines from the standard matrix equation in Lehtinen and Pirjola (1985): mathbf{I} = left(mathbf{1} + mathbf{Y}mathbf{Z}right)^{-1} cdot mathbf{J} (3).

Hence, we seek a solution of the matrix equation in the following form: U j = α j + 1 U j + 1 + β j + 1, j = M − 1, …, 2, 1, (3.7).