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On the extended direct sum conjecture
Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89, 1989We consider the quadratic complexity of certain sets of quadratic forms. We study a classes of direct sums of quadratic forms. For these classes of problems we show that the complexity of one direct sum is the sum of the complexity of the summands and that every minimal quadratic algorithm for computing the direct sums is a direct-sum algorithm.
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2002
If A and B are non-empty subsets of a vector space V over a field F then the subspace spanned by A ∪ B, i.e. the smallest subspace of V that contains both A and B, is the set of linear combinations of elements of A ∪ B. In other words, it is the set of elements of the form $$ [\sum\limits_{i = 1}^m {{\lambda _i}} {a_i} + \sum\limits_{j = 1}^n {{\mu
T. S. Blyth, E. F. Robertson
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If A and B are non-empty subsets of a vector space V over a field F then the subspace spanned by A ∪ B, i.e. the smallest subspace of V that contains both A and B, is the set of linear combinations of elements of A ∪ B. In other words, it is the set of elements of the form $$ [\sum\limits_{i = 1}^m {{\lambda _i}} {a_i} + \sum\limits_{j = 1}^n {{\mu
T. S. Blyth, E. F. Robertson
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2002
In Theorem 2.6 we obtained, for an inner product space V and a finite-dimensional subspace W of V, a direct sum decomposition of the form V = W ⊕W⊥. We now consider the following general notion.
T. S. Blyth, E. F. Robertson
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In Theorem 2.6 we obtained, for an inner product space V and a finite-dimensional subspace W of V, a direct sum decomposition of the form V = W ⊕W⊥. We now consider the following general notion.
T. S. Blyth, E. F. Robertson
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Modules Over Trusses vs Modules Over Rings: Direct Sums and Free Modules
Algebras and Representation Theory, 2022Tomasz Brzeziński, Bernard Rybołowicz
exaly
Direct sums of cyclic summands
Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1983Doyle, Cutler +3 more
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Uniform Convexity of ψ-Direct Sums of Banach Spaces
Journal of Mathematical Analysis and Applications, 2003Kichi-Suke Saito, Mikio Kato
exaly