منابع مشابه
On Matrices with Signed Null-Spaces
We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A has signed null-space provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null-space of à is S for each à ∈ Q(A). Some properties of matrices with signed null-spaces are investigated.
متن کاملSome properties of matrices with signed null spaces
A matrix A is said to have signed null space provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null space of à is S for each Ã∈Q(A). It is a generalization of a number of important qualitative matrix classes such as L-matrices, S∗-matrices, totally L-matrices, etc. In this paper, we obtain some new characterizations for matrices with signed null...
متن کاملOn the Computation of Null Spaces of Sparse Rectangular Matrices
Computing the null space of a sparse matrix, sometimes a rectangular sparse matrix, is an important part of some computations, such as embeddings and parametrization of meshes. We propose an efficient and reliable method to compute an orthonormal basis of the null space of a sparse square or rectangular matrix (usually with more rows than columns). The main computational component in our method...
متن کاملOn Positive Matrices Which Have a Positive Smith Normal Form
It is known that any symmetric matrix M with entries in R[x] and which is positive semi-definite for any substitution of x ∈ R, has a Smith normal form whose diagonal coefficients are constant sign polynomials in R[x]. We generalize this result by considering a symmetric matrix M with entries in a formally real principal domain A, we assume that M is positive semi-definite for any ordering on A...
متن کاملOn Metric Spaces in Which Metric Segments Have Unique Prolongations
An M-space is a metric space (X, d) having the property that for each pair of points p, q ∈ X with d(p, q) = λ and for each real number α ∈ [0, λ], there is a unique rα ∈ X such that d(p, rα) = α and d(rα, q) = λ − α. In an M-space (X, d), we say that metric segments have unique prolongations if points p, q, r, s satisfy d(p, q) + d(q, r) = d(p, r), d(p, q) + d(q, s) = d(p, s) and d(q, r) = d(q...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2002
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(02)00312-9