It is proved that there is no an algorithm for multiplication of $3\times3$ matrices of multiplicative length $\leq23$ that is invariant under a certain group isomorphic to $S_4\times S_3$. The proof makes use of description of the orbits of this group on decomposable tensors in the tensor cube $(M_3({\mathbb C}))^{\otimes3}$ which was obtained earlier.Comment: 13 pp. Accepted for publication in Proceedings of the Institute of Mathematics of Academy of Sciences of Belaru
AbstractAfter the change of variables Δi = γi − δi and xi,i + 1 = δi − δi + 1 we show that the invar...
Let $K$ be a field of characteristic $p > 2$ and let $G$ be a group. Necessary and sufficient con...
Representation Theory of Algebraic Groups and Related Topics : Proceedings of the workshop on Repres...
One of prospective ways to find new fast algorithms of matrix multiplication is to study algorithms ...
All decompositions of $M_3(\mathbb{C})$ into a direct vector-space sum of two subalgebras such that ...
This is the second in a series of papers on rank decompositions of the matrix multiplication tensor....
The exponent of matrix multiplication is the smallest real number ω such that for all ε>0, O(n^(ω+ε)...
The Cayley map for the rotation group SO(3) is extended to a map from the Lie algebra of the group o...
AbstractMirsky proved that, for the existence of a complex matrix with given eigenvalues and diagona...
AbstractLet Cu(γ) be the minimal number of cubes required to express an element γ of a free group F....
AbstractRecently, Ito and Terwilliger proposed a problem about some linear transformations A+,A-,A+∗...
AbstractLet A be n×n matrix of rank r. Then xn−r divides the characteristic polynomial det(xI−A) of ...
AbstractLet F be an arbitrary field, H be a subgroup of the symmetric group of degree m, Sm, λ be an...
We present a non-commutative algorithm for the multiplication of a block-matrix by its transpose ove...
AbstractA necessary condition is given for the existence of an O-basis for the symmetry classes of t...
AbstractAfter the change of variables Δi = γi − δi and xi,i + 1 = δi − δi + 1 we show that the invar...
Let $K$ be a field of characteristic $p > 2$ and let $G$ be a group. Necessary and sufficient con...
Representation Theory of Algebraic Groups and Related Topics : Proceedings of the workshop on Repres...
One of prospective ways to find new fast algorithms of matrix multiplication is to study algorithms ...
All decompositions of $M_3(\mathbb{C})$ into a direct vector-space sum of two subalgebras such that ...
This is the second in a series of papers on rank decompositions of the matrix multiplication tensor....
The exponent of matrix multiplication is the smallest real number ω such that for all ε>0, O(n^(ω+ε)...
The Cayley map for the rotation group SO(3) is extended to a map from the Lie algebra of the group o...
AbstractMirsky proved that, for the existence of a complex matrix with given eigenvalues and diagona...
AbstractLet Cu(γ) be the minimal number of cubes required to express an element γ of a free group F....
AbstractRecently, Ito and Terwilliger proposed a problem about some linear transformations A+,A-,A+∗...
AbstractLet A be n×n matrix of rank r. Then xn−r divides the characteristic polynomial det(xI−A) of ...
AbstractLet F be an arbitrary field, H be a subgroup of the symmetric group of degree m, Sm, λ be an...
We present a non-commutative algorithm for the multiplication of a block-matrix by its transpose ove...
AbstractA necessary condition is given for the existence of an O-basis for the symmetry classes of t...
AbstractAfter the change of variables Δi = γi − δi and xi,i + 1 = δi − δi + 1 we show that the invar...
Let $K$ be a field of characteristic $p > 2$ and let $G$ be a group. Necessary and sufficient con...
Representation Theory of Algebraic Groups and Related Topics : Proceedings of the workshop on Repres...
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