Sentence examples for matrices we prove from inspiring English sources
With the aid of techniques of differential calculus, Hadamard's and Fisher's inequalities for symmetric and positive definite matrices, we prove that the conjecture is true for n autocorrelated observations and k two-level factors with n = 4ν and k = 2.
Based on finite-time Lyapunov stability theorem and matrix theory, we prove that the finite-time consensus of high-order uncertain nonlinear multi-agent systems is guaranteed by non-lipschitz continuous control laws.
Applying results from random matrix theory, we prove that for such a DAS, the per-user sum rate and the total transmit power both converge as user number and antenna number go to infinity with a constant ratio.
(1.7) In Section 2 for this subclass of matrices we will prove the following.
By using the resolvent operator due to Lan-Cho-Verma associated with -accretive mappings and the matrix analysis method, we prove the convergence of a new hybrid proximal point three-step iterative algorithm for this system of set-valued variational inclusions and an existence theorem of solutions for this kind of the variational inclusions system.
Assuming that the discrete maximum principle (d.m.p). is satisfied, i.e. the matrix resulting from the finite element discretization is an M-matrix (see [18, 19]), we prove the Lipschitz discrete dependence with respect to both the boundary condition and the source term by a similar study to that undertaken previously for the Lipschitz continuous dependence property.
Next, we prove the following matrix version of Heinz inequality for the Hilbert-Schmidt norm.
In addition, we prove that the constructed matrices can be almost completely incoherent with the conventional wavelet dictionary.
We prove that a positive matrix with all permutation products equal is diagonally equivalent to J, the all-1s matrix.
We prove that such a matrix has rank at most 2 and that any square submatrix of a diagonally magic matrix is diagonally magic.
Here, we prove a numerical radius equality for a special (5times5) tridiagonal operator matrix and then we prove a more general numerical radius inequality for the general (5times5) tridiagonal operator matrix.
