Sentence examples for matrix there exists from inspiring English sources

It is found that, contrary to the case where the inclusion is embedded in an infinite-size matrix, there exists near the free-surface a preferential plane selected for the dipole formation in the interface which corresponds to the plane perpendicular to the free surface and containing the inclusion centre.

With regard to matrix, there exists an invertible matrix, such that (3.4).

Since is a diagonalization matrix, there exists an invertible matrix such that (2.8).

A is a Schur matrix; There exists vector (vsucc0) in (Re^{n}) with ((A-I vprec0). A-I vprec0

Moreover, it holds for negative definite Hermite matrices, even for any invertible Hermite matrix, there exists a similar inequality.

It is known that, for every matrix, there exists a nonsingular matrix transforming it to the corresponding Jordan matrix form.

For any realization of channel matrix, there exist unique values of the Lagrange dual variables and for any Nash equilibrium of the game.

One fact is that for a given transfer function matrix, there exist infinite number of state space representations related by a similarity transform.

For a general tensor matrix, there exist two orthogonal vectors (known as eigenvectors) that represent the directions of the beam's maximal and minimal stiffness.

We next assume that n ≥ 2. Since A is an M-matrix, there exists a positive diagonal matrix D such that D − 1 A D is a strictly row diagonally dominant M-matrix, and τ ( B ∘ A − 1 ) = τ ( D − 1 ( B ∘ A − 1 ) D ) = τ ( B ∘ ( D − 1 A D ) − 1 ).

Since A is an M-matrix, there exists a positive diagonal matrix X, such that (X^{-1}AX) is a strictly row diagonally dominant M-matrix (see [2]), and rhobigl Bcirc A^{-1}bigr)=rhobigl(X^{-1}bigl Bcirc A^{-1}bigr)X^{-1}bigl Bcirccircbigl(X^{-1}AX bigr)^{-1}bigr).