Sentence examples for matrix with positive from inspiring English sources
Another class is constituted by materials consisting of a matrix with positive Poisson's ratio with embedded microstructural elements producing macroscopic negative Poisson's ratio.
Explosive modes such as ignition and extinction are characterized by an eigenvalue of the chemical Jacobian matrix with positive real part, representing the transient instability of chain-branching chemistry and thermal feedback.
Obviously (x_{i}neq+infty), then X is a diagonal matrix with positive diagonal entries.
As (varepsilonneq+infty), so (x_{i}neq+infty), which implies that X is a diagonal matrix with positive entries.
where Γ is a diagonal matrix with positive diagonal elements and φ is in (Gamma _{0}(mathbb {R}^{m+1})).
By the irreducibility of (mathcal{A}), we have (x_{i}neq+infty), then X is a diagonal matrix with positive diagonal entries.
We generalize the Nevanlinna representation theorems and Löwner's theorem on matrix monotone functions to the free Pick class, the collection of functions that map tuples of matrices with positive imaginary part into the matrices with positive imaginary part which obey the free functional calculus.
Notice that (tilde{B}_{D}^) is an SDD Z-matrix with positive diagonal entries, and thus (tilde{B}_{D}^) is an SDD M-matrix.
According to Definition 1.3, (underline{Phi}) is a H-matrix with positive diagonal elements, it is to say (underline{Phi}>0).
Similarly to the proof of Theorem 2.2 in [2], we find that (B_{D}^) is an SDD M-matrix with positive diagonal elements and that big| M_{D}^{-1}big| _{infty}leqslantbig| bigl(I + bigl(B^_{D}bigr)^{-1}C_{D} bigr)^{-1} big| _{infty}big| bigl(B^_{D} bigr)^{-1} big| _{infty}leqslant n-1) big| bigl(B^_{infty}leqslant n-1 _{infty}.
Similar to the proof of Theorem 2 in [13], we see that (B_{D}^) is a wcdd M-matrix with positive diagonal elements and (C_{D}=DC), and, by Lemma 1, biglVert M_{D}^{-1}bigrVert _{infty}leq biglVert bigl(I+bigl(B_{D}^bigr)^{-1}C_{D} bigr)^{-1}bigrVert _{infty} biglVert bigl(B_{D}^ bigr)^{-1}bigrVert _{infty} leq (n-1 biglVert n-1 biglVertigr)^{-1}biglVert _{infty}.
