Sentence examples for matrices given in from inspiring English sources

The proof is based on the uniformity property of transfer matrices given in Lemma 1 together with counting.

Now we focus our attention to the case of (1.2) for being weighted mean matrices given in (1.3).

The following discussion makes use of the important properties of circulant matrices given in the appendices (Facts 1 and 2).

We also thank the anonymous reviewers for their comments and one in particular for suggesting the useful formal definition of disambiguation matrices given in the Methods section.

The MVN densities can be calculated efficiently with the diagonalization matrices given in step 1.

To calculate the capacity of the molecular channel, one needs the transition probability channel matrix M. Depending on which molecule is dominant in the pathological channel, one can use the matrices given in (12 - 16 12 - 16

Let Z be the K×K matrix given in (7).

The D w matrix given below is the watermarked D matrix given in Equation (2).

Note that, for (r=1), geometric circulant matrix turns into circulant matrix given in [11, 12].

It can be calculated by the method of next generation matrix given in [32].

The MIMO LE matrix given in (12) has implicit forms which are difficult for evaluation.