Word embedding in form of symmetric and skew-symmetric operator

Given a positive integer n ≥ 5, what is the relationship between two skew-symmetric matrices of orders n which differ up to the sign of their off-diagonal terms and having

Their main theorem implies that two symmetric matrices have equal corresponding principal minors of all orders if and only if they are diagonally similar.. This study was continued

To compare with the proof of [HMV, Theorem 14.1] which deals with minimal linear description (for symmetric non-commutative polynomials) although they are not given by

By producing fluctua- tions of density near the critical point like in computational molecular dynamics, the model is more realistic and richer than van der Waals’ one and other

This class of superalgebras includes for instance Lie algebras and their n-ary generalizations, commutative associative and Jordan algebras with invariant forms.. We give

Consider any radial line (line going through the distortion center) in the first image; the projection rays associated with the points on that line are necessarily coplanar according

We give noncommutative versions of the Redfield-P´ olya theorem in WSym, the algebra of word symmetric functions, and in other re- lated combinatorial Hopf algebras..

Unfortunately, this approach suffers two drawbacks: its time and space requirements might become prohibitive if the optimal mixture of policies is composed of too many policies, and