共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
B. Kuzma 《Linear and Multilinear Algebra》2013,61(4):231-241
Additive mappings, which do not increase the minimal rank of alternate matrices, are completely classified. No condition is imposed on the underlying field. 相似文献
3.
B. Kuzma 《Linear and Multilinear Algebra》2005,53(4):231-241
Additive mappings, which do not increase the minimal rank of alternate matrices, are completely classified. No condition is imposed on the underlying field. 相似文献
4.
5.
Let T be a linear operator on the space of all m×n matrices over any field. we prove that if T maps rank-2 matrices to rank-2 matrices then there exist nonsingular matrices U and V such that either T(X)=UXV for all matrices X, or m=n and T(X)=UXtV for all matrices X where Xt denotes the transpose of X. 相似文献
6.
Let T be a linear operator on the space of all m×n matrices over any field. we prove that if T maps rank-2 matrices to rank-2 matrices then there exist nonsingular matrices U and V such that either T(X)=UXV for all matrices X, or m=n and T(X)=UXtV for all matrices X where Xt denotes the transpose of X. 相似文献
7.
In this paper, we characterize (i) linear transformations from one space of Boolean matrices to another that send pairs of distinct rank one elements to pairs of distinct rank one elements and (ii) surjective mappings from one space of Boolean matrices to another that send rank one matrices to rank one matrices and preserve order relation in both directions. Both results are proved in a more general setting of tensor products of two Boolean vector spaces of arbitrary dimension. 相似文献
8.
Zero-term rank preservers 总被引:2,自引:0,他引:2
We obtain characterizations of those linear operators that preserve zero-term rank on the m×n matrices over antinegative semirings. That is, a linear operator T preserves zero-term rank if and only if it has the form T(X)=P(B∘X)Q, where P, Q are permutation matrices and B∘X is the Schur product with B whose entries are all nonzero and not zero-divisors. 相似文献
9.
10.
Raphael Loewy 《Linear and Multilinear Algebra》2001,48(4):355-382
Let k and n be positive integers such that k≤n. Let Sn(F) denote the space of all n×n symmetric matrices over the field F with char F≠2. A subspace L of Sn(F) is said to be a k-subspace if rank A≤k for every AεL.
Now suppose that k is even, and write k=2r. We say a k∥-subspace of Sn(F) is decomposable if there exists in Fn a subspace W of dimension n-r such that xtAx=0 for every xεWAεL.
We show here, under some mild assumptions on kn and F, that every k∥-subspace of Sn(F) of sufficiently large dimension must be decomposable. This is an analogue of a result obtained by Atkinson and Lloyd for corresponding subspaces of Fm,n. 相似文献
Now suppose that k is even, and write k=2r. We say a k∥-subspace of Sn(F) is decomposable if there exists in Fn a subspace W of dimension n-r such that xtAx=0 for every xεWAεL.
We show here, under some mild assumptions on kn and F, that every k∥-subspace of Sn(F) of sufficiently large dimension must be decomposable. This is an analogue of a result obtained by Atkinson and Lloyd for corresponding subspaces of Fm,n. 相似文献
11.
Martin Argerami Fernando Szechtman Ryan Tifenbach 《Linear and Multilinear Algebra》2007,55(6):515-520
The problem of whether Tate's trace is linear or not is reduced to a special case. 相似文献
12.
Let Tn (F) be the algebra of all n×n upper triangular matrices over an arbitrary field F. We first characterize those rank-one nonincreasing mappings ψ: Tn (F)→Tm (F)n?m such that ψ(In ) is of rank n. We next deduce from this result certain types of singular rank-one r-potent preservers and nonzero r-potent preservers on Tn (F). Characterizations of certain classes of homomorphisms and semi-homomorphisms on Tn (F) are also given. 相似文献
13.
Additive mappings, which do not increase the minimal rank of symmetric matrices are classified in characteristic two or three. 相似文献
14.
《Linear and Multilinear Algebra》2007,55(6):521-533
For each k≥ 0, those nonsingular matrices that transform the set of totally nonzero vectors with k sign variations into (respectively, onto) itself are studied. Necessary and sufficient conditions are provided. The cases k=0,1,2,n-3,n-2,n-1 are completely characterized. 相似文献
15.
Xian Zhang 《Linear and Multilinear Algebra》2004,52(5):349-358
Suppose F is a field of characteristic not 2. Let MnF and SnF be the n × n full matrix space and symmetric matrix space over F, respectively. All additive maps from SnF to SnF (respectively, MnF) preserving Moore-Penrose inverses of matrices are characterized. We first characterize all additive Moore-Penrose inverse preserving maps from SnF to MnF, and thereby, all additive Moore-Penrose inverse preserving maps from SnF to itself are characterized by restricting the range of these additive maps into the symmetric matrix space. 相似文献
16.
Yongge Tian 《Linear and Multilinear Algebra》2002,49(4):269-288
A matrix X is called an outer inverse for a matrix A if XAX=X. In this paper, we present some basic rank equalities for difference and sum of outer inverses of a matrix, and apply them to characterize various equalities related to outer inverses, Moore-Penrose inverses, group inverses, Drazin inverses and weighted Moore-Penrose inverses of matrices. 相似文献
17.
Yongge Tian 《Linear and Multilinear Algebra》2013,61(4):269-288
A matrix X is called an outer inverse for a matrix A if XAX=X. In this paper, we present some basic rank equalities for difference and sum of outer inverses of a matrix, and apply them to characterize various equalities related to outer inverses, Moore-Penrose inverses, group inverses, Drazin inverses and weighted Moore-Penrose inverses of matrices. 相似文献
18.
Yongge Tian 《Linear and Multilinear Algebra》2005,53(1):45-65
Some results on the Moore-Penrose inverse for sums of matrices under rank additivity conditions are revisited and some new consequences are presented. Their extensions to the weighted Moore-Penrose inverse of sums of matrices under rank additivity conditions are also considered. 相似文献
19.
The problem of whether Tate's trace is linear or not is reduced to a special case. 相似文献
20.
Rajesh Pereira 《Linear algebra and its applications》2011,435(7):1666-1671
We classify the bijective linear operators on spaces of matrices over antinegative commutative semirings with no zero divisors which preserve certain rank functions such as the symmetric rank, the factor rank and the tropical rank. We also classify the bijective linear operators on spaces of matrices over the max-plus semiring which preserve the Gondran-Minoux row rank or the Gondran-Minoux column rank. 相似文献