As we mature from childhood, our vocabulary—as well as the ways we use it—grows, and our experiences become richer, allowing ...

We characterize all such algebras: if a matrix algebra A does not share invariant subspaces with its commutant, then it must be similar to an amplification of a full matrix algebra. Then, we show that ...

Don Deckard, R. G. Douglas, Carl Pearcy, On Invariant Subspaces of Quasitriangular Operators, American Journal of Mathematics, Vol. 91, No. 3 (Jul., 1969), pp. 637-647. Free online reading for over 10 ...

Key takeawaysA new study that compares biological brains with artificial intelligence systems analyzed the neural network patterns that emerged during ...