Sentence examples for determinant theorem from inspiring English sources

where we again applied Sylvester's determinant theorem.

where (105) and (107) follow from Sylvester's determinant theorem.

Assuming well-conditioned channel matrices and using Sylvester's determinant theorem [12], the k th user rate can be approximated for high SNR values by R k ≈ SNR ≫ 1 log 2 p H kk W V k V k H W H H kk H U k H U k. (16).

We start by applying Sylvester's determinant theorem and Jensen's inequality to (24): begin{array}{*{20}l} tilde{R}_{u} leq text{ log} left|sigma_{n,u}^{2} mathbf{I}_{N_{t}} + mathbb{E}left({{mathbf{H}_{u}^{mathrm{H}}} mathbf{H}_{u} sum_{j in mathcal{S}} mathbf{F}_{j} {mathbf{F}_{j}^{mathrm{H}}}}right)right| end{array} (34).

Using the Sylvester's determinant theorem [12], the fact that all channel matrices are diagonal, and the definition of B k and A k as B k = ∑ j = 1, j ≠ k K H kj V j V j H H kj H A k = B k + H kk V k V k H H kk H, (10).

For these results in this paper, one can obtain much sharper estimates on determinants by computing the signs of determinants using Theorem 2.2.

We start with what is generally agreed to be the most compelling unresolved question in the subject of Leavitt path algebras, stated concisely as: The Algebraic Kirchberg Phillips Question: Can we drop the hypothesis on the determinants in Theorem 23?

The analogous question about Morita equivalence asks whether or not we can drop the determinant hypothesis from Theorem 22.

\(\qed\) Theorem (Gärdenfors' Triviality Theorem).

By Theorem 3.2 the determinant (D z), zin {mathbb D}), is analytic and Höder up to the boundary.

Due to Theorem 2.1 the determinant D z) is analytic in ({mathbb D}) and Höder up to the boundary.