Sentence examples for matrix equals the from inspiring English sources
Our matrix equals the conjugate-transpose of their definition.
where is the adjoint matrix of, which is the transpose of the minors of since the cofactor matrix equals the minors matrix in the binary field.
As a result, and by using the property that the trace of a matrix equals the sum of its eigenvalues, then ω 1 could be written as begin{array}{*{20}l} omega_{1} &= text{tr}(mathbf{Omega}_{K})= frac{1}{sigma_{eta}^{2}}lVert boldsymbol{s} rVert^{2} text{tr}left(boldsymbol{h}boldsymbol{h}^{dagger}right) = frac{1}{sigma_{eta}^{2}}lVert boldsymbol{s} rVert^{2}lVert boldsymbol{h} rVert^{2} &= NKrho.
The matrix equals the times the pathway matrix (P) with the contribution of its i th SNP (row) removed.
Hence, Eq. (12) must exist because it describes all linear combinations of independent fluxes (J I ) that give rise to the dependent fluxes in J D : 12 Thus, the right null-space of the (reduced) stoichiometry matrix equals the kernel matrix, given by Eq. (13): 13 Note that the columns of N R may have to be reordered to write the null-space in this form.
The determinant of a product of square matrices equals the product of their determinants: :det(AB) = det(A) · det(B).
The parabolic free energy, that approximates the bulk free energy, is parameterized such that the resulting chemical potential in the matrix equals its counterpart from the ideal solution free energy (Eq. 5), e.g., 2 Bc=frac{k_{mathrm{B}}T}{Omega}ln frac{c_{mathrm{v}}}{c_{mathrm{v}}^{mathrm{eq}}}.
Consider now that (1) Whitening reduces the BSS problem to finding an orthogonal demixing matrix ; (2) equals the cross-covariance matrix of the source components S at time-lag τ; and (3) The independence assumption yields that the cross-covariance matrix of the source components S at time-lag τ is a diagonal matrix.
The number of columns of this matrix apparently equals the number of nodes n in the network.
The value of a matrix element equals the parameter value (Fig. 3B).
Using these operations, any matrix can be transformed to a lower (or upper) triangular matrix, and for such matrices the determinant equals the product of the entries on the main diagonal; this provides a method to calculate the determinant of any matrix.
