共查询到20条相似文献,搜索用时 15 毫秒
1.
Henryk Minc 《Linear and Multilinear Algebra》1977,4(4):265-272
A theorem of Marcus and Moyls on linear transformations on matrices preserving rank 1 and a classical result of Frobenius on determinant preservers are re-proved by elementary matrix methods. 相似文献
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It is proved that a linear transformation on the vector space of upper triangular matrices that maps the set of matrices of minimal rank 1 into itself, and either has the analogous property with respect to matrices of full minimal rank, or is bijective, is a triangular equivalence, or a flip about the south-west north-east diagonal followed by a triangular equivalence. The result can be regarded as an analogue of Marcus–Moyls theorem in the context of triangular matrices. 相似文献
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Kyung-Tae Kang 《Linear and Multilinear Algebra》2013,61(2):241-247
We obtain some characterizations of linear operators that preserve the term rank of Boolean matrices. That is, a linear operator over Boolean matrices preserves the term rank if and only if it preserves the term ranks 1 and k(≠1) if and only if it preserves the term ranks 2 and l(≠2). Other characterizations of term rank preservers are given. 相似文献
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Sara M. Motlaghian Ali Armandnejad Frank J. Hall 《Czechoslovak Mathematical Journal》2016,66(3):847-858
Let Mm,n be the set of all m × n real matrices. A matrix A ∈ Mm,n is said to be row-dense if there are no zeros between two nonzero entries for every row of this matrix. We find the structure of linear functions T: Mm,n → Mm,n that preserve or strongly preserve row-dense matrices, i.e., T(A) is row-dense whenever A is row-dense or T(A) is row-dense if and only if A is row-dense, respectively. Similarly, a matrix A ∈ Mn,m is called a column-dense matrix if every column of A is a column-dense vector. At the end, the structure of linear preservers (strong linear preservers) of column-dense matrices is found. 相似文献
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We characterize linear operators on matrices over semirings that preserve the extremal cases in the bounds on term and zero-term
ranks of sums and products of matrices.
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Translated from Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 2, pp. 3–21,
2004. 相似文献
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Let F be a field with ∣F∣ > 2 and Tn(F) be the set of all n × n upper triangular matrices, where n ? 2. Let k ? 2 be a given integer. A k-tuple of matrices A1, …, Ak ∈ Tn(F) is called rank reverse permutable if rank(A1 A2 ? Ak) = rank(Ak Ak−1 ? A1). We characterize the linear maps on Tn(F) that strongly preserve the set of rank reverse permutable matrix k-tuples. 相似文献
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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
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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
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Linear transformations on symmetric matrices 总被引:1,自引:0,他引:1
M. H. Lim 《Linear and Multilinear Algebra》1979,7(1):47-57
In this paper we study the problem of characterizing those linear transformations on the vector space of symmetric matrices which preserve a fixed rank or the signature. 相似文献
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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
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Let Tbe a linear mapping on the space of n× nsymmetric matrices over a field Fof characteristic not equal to two. We obtain the structure of Tfor the following cases:(i) Tpreserves matrices of rank less than three; (ii) Tpreserves nonzero matrices of rank less than K + 1 where Kis a fixed positive integer less than nand Fis algebraically closed; (iii) Tpreserves rank Kmatrices where Kis a fixed odd integer and Fis algebraically closed. 相似文献
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Let 𝔽 be a field of characteristic two. Let S n (𝔽) denote the vector space of all n?×?n symmetric matrices over 𝔽. We characterize i. subspaces of S n (𝔽) all whose elements have rank at most two where n???3, ii. linear maps from S m (𝔽) to S n (𝔽) that sends matrices of rank at most two into matrices of rank at most two where m, n???3 and |𝔽|?≠?2. 相似文献
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Kyung-Tae Kang Seok-Zun Song LeRoy B. Beasley 《Linear algebra and its applications》2012,436(7):1850-1862
The term rank of a matrix over a semiring is the least number of lines (rows or columns) needed to include all the nonzero entries in . In this paper, we study linear operators that preserve term ranks of matrices over . In particular, we show that a linear operator on matrix space over preserves term rank if and only if preserves term ranks and if and only if preserves two consecutive term ranks in a restricted condition. Other characterizations of term-rank preservers are also given. 相似文献