Sentence examples for matrices are distinct from inspiring English sources

An advantage of this approach is that most of the Lyapunov matrices are distinct with respect to system mode and thus the choice of these matrices becomes much flexible.

The authors in [30] consider the case where all the eigenvalues of the correlation matrix are distinct.

The proof of the following statement (which shows the non-emptiness of the central stability zone under an additional assumption that the eigenvalues of a certain matrix are distinct) is essentially the same as that of [[2], Theorem 2.2].

For instance, two squares in the middle of the matrix are distinct yet appear more similar to each other than any other pair of consecutive contigs.

Remark 2.3 For any positive integer a ≥ 2, the eigenvalues S d, 0, a − 1 S d, 0, a − 2 S d, 0, …, a − m S d, 0 of the matrix (1) are distinct.

If all columns of a frequency matrix F are distinct then the ancestry graph G is a DAG.

O bservation 1 If all columns of a frequency matrix F are distinct then the ancestry graph G is a DAG.

Recall that a monomial vector is a (nonzero) multiple of some canonical basis vector, and a monomial matrix M is a matrix whose columns are distinct monomial vectors and can be decomposed as M = D P where D is a diagonal matrix and P is a permutation matrix.

Nevertheless, it is enough to observe that the cycles depend on the monotonically increasing function in (2.2). has two fixed points if and only if the eigenvalues of the matrix in (2.4) are distinct real numbers.

In particular, HIV matrices define substitution patterns that are distinct from all other empirical models at several evolutionary time-scales.

However, this form is applicable if the array is small and the eigenvalues of the covariance matrix of the observed data are distinct.