Sentence examples for existence of a matrix from inspiring English sources

Furthermore, condition (3.28) assures the existence of a matrix function such that condition (3.18) is fulfilled.

Studies concerning the connection of frames with graphs have shown that the existence of an ETF in a real Hilbert space depends on the existence of a matrix Q with zero diagonal and ± 1's off-diagonal entries.

This is equivalent to the existence of a matrix A ∈ R m × n such that C = { x : A x ≥ 0}.

Our morphological findings show the existence of a matrix degradation and cell remodelling mechanism in colorectal adenocarcinomas that involves both IPCs and epithelial cells.

If we let the rank of S be denoted by n r, the number of linearly independent vectors for which Eq. (7) holds is equal to n - n r, which implies the existence of a matrix M (8) M S = 0, where M ∈ ℕ n - n r × n.

Our new approach allows us to find the necessary and sufficient conditions for the existence of such a matrix.

Constructions of such designs are presented, given the existence of an Sn matrix and a Hadamard matrix.

The diffusion model was applied to concentrated perfume mixtures but also to quaternary mixtures, considering the existence of a solvent matrix (ethanol).

In other words, we investigate the problem of existence of a diagonal matrix (D=operatorname{diag}(x_{1},ldots,x_{n},x_{n})) with (x_{i}>0) and with the property A^{T}D+DA< 0 quad mbox{for all } A inmathcal{A}.

In this article, we provide a graph-theory approach to find the necessary and sufficient conditions for the existence of a phylogeny matrix with k nonidentical haplotypes, n single nucleotide polymorphisms (SNPs), and a population size of m for which the minimum allele frequency of each SNP is between two specific numbers a and b.

The existence of a smallB-matrix is also proved.