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Canadian Journal of Mathematics, 1960
Let A, B, and X be n-square matrices over an algebraically closed field F of characteristic 0. Let [A, B] = AB — BA and set (A, B) = [A, [A, B]]. Recently several proofs (1; 3; 5) of the following result have appeared: if det (AB) ≠ 0 and (A,B) = 0 then A-1B-1AB - I is nilpotent.
Marcus, Marvin, Khan, Nisar A.
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Let A, B, and X be n-square matrices over an algebraically closed field F of characteristic 0. Let [A, B] = AB — BA and set (A, B) = [A, [A, B]]. Recently several proofs (1; 3; 5) of the following result have appeared: if det (AB) ≠ 0 and (A,B) = 0 then A-1B-1AB - I is nilpotent.
Marcus, Marvin, Khan, Nisar A.
openaire +2 more sources
Canadian Journal of Mathematics, 1963
The following elementary facts about certain commutative diagrams, called "squares," are stated and proved in terms of abelian groups and their homomorphisms. However, they are valid for arbitrary abelian categories and can be proved also for them. This does not need to be shown, since every abelian category can be embedded into the category of abelian
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The following elementary facts about certain commutative diagrams, called "squares," are stated and proved in terms of abelian groups and their homomorphisms. However, they are valid for arbitrary abelian categories and can be proved also for them. This does not need to be shown, since every abelian category can be embedded into the category of abelian
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American Journal of Mathematics, 1952
A mathematical formulation of the famous Heisenberg uncertainty principle is that a certain pair of linear transformations P and Q satisfies, after suitable normalizations, the equation PQ - QP = 1. It is easy enough to produce a concrete example of this behavior; consider L2(-∞, +∞) and let P and Q be the differentiation transformation and the ...
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A mathematical formulation of the famous Heisenberg uncertainty principle is that a certain pair of linear transformations P and Q satisfies, after suitable normalizations, the equation PQ - QP = 1. It is easy enough to produce a concrete example of this behavior; consider L2(-∞, +∞) and let P and Q be the differentiation transformation and the ...
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18th Annual Symposium on Foundations of Computer Science (sfcs 1977), 1977
In this paper we show that the computation of the determinant requires an exponential number of multiplications if the commutativity of indeterminates is not allowed. The determinant can be computed in polynomial time with the commutation of indeterminates.
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In this paper we show that the computation of the determinant requires an exponential number of multiplications if the commutativity of indeterminates is not allowed. The determinant can be computed in polynomial time with the commutation of indeterminates.
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Commutativity, non-commutativity, and bilinearity
Information Processing Letters, 1976openaire +2 more sources
On Commutativity of Rings With Derivations
Resultate Der Mathematik, 2013Mohammad Ashraf +2 more
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Commutativity preserving maps on quantum states
Reports on Mathematical Physics, 2009Gergo Nagy
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Commutativity of k th -order slant Toeplitz operators
Mathematische Nachrichten, 2010Yufeng Lu, Chaomei Liu
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