Nicholas Clifford Maino

The Commutator of Two Companion Matrices Has Rank at Most Two, with Spectral Consequences over Arbitrary Fields

We prove that the commutator [U,Q] = UQ − QU of two n×n companion matrices has rank at most two, over an arbitrary field, by exhibiting an explicit decomposition of [U,Q] as a sum of two rank-one matrices. The mechanism is not special to companion matrices: for any A and any e, t...

The Commutator of Two Companion Matrices Has Rank at Most Two, with Spectral Consequences over Arbitrary Fields

We prove that the commutator [U,Q] = UQ − QU of two n×n companion matrices has rank at most two, over an arbitrary field, by exhibiting an explicit decomposition of [U,Q] as a sum of two rank-one matrices. The mechanism is not special to companion matrices: for any A and any e, t...

The Curl of the Vorticity, Not the Vorticity, Controls Hawking–Ellis Type IV in Warp Spacetimes

Recent work identifies the vorticity of the ADM shift as the geometric quantity controlling theHawking-Ellis algebraic type of warp-drive stress-energy, with the Type-IV imaginary eigenvalueobeying f = kappa*omega in a controlled limit, while reporting that kappa depends on wall...

The Curl of the Vorticity, Not the Vorticity, Controls Hawking–Ellis Type IV in Warp Spacetimes

Recent work identifies the vorticity of the ADM shift as the geometric quantity controlling theHawking-Ellis algebraic type of warp-drive stress-energy, with the Type-IV imaginary eigenvalueobeying f = kappa*omega in a controlled limit, while reporting that kappa depends on wall...