I finally learned that
MATLAB uses the apostrophe operator (') to perform a complex conjugate transpose, and the dot-apostrophe operator (.') to transpose without conjugation¹.despite my unshakable-yet-painfully-mistaken belief that the converse was true.
One nice outcome— the .' versus ' distinction caused an oscillating phase symptom that made me go through my formulation in detail. I added the derivation as as a nonlinear example on Wikipedia's spectral method page. It will be interesting to see how long the edit survives.
Frustratingly, MATLAB's M-script is only half a hair more predictable than PHP. That ones(1); ans(1) returns one but ones(1)(1) is a syntax error boggles my mind.