## Archive for May, 2013

### on morphological types

I tend to reject the classification of languages onto the analytic-synthetic spectrum. I don’t think such a spectrum exists beyond a superficial level. Recall that this classification depends on the morphemes-per-word ratio, and as such, depends on the putative existence of “words”, i.e., that there are so-called bound morphemes making up multi-morpheme words in synthetic languages. What makes these morphemes especially more “bound” in synthetic languages? The fact that even in a purely analytic language, free morphemes are not really free in the sense that they must be arranged in some order with some grammar to make meaning, suggests that there is really no fundamental difference between analytic and synthetic languages. All morphemes are bound to one degree or another. Whether they can be uttered in isolation is more about function.
$$A$$ and $$B$$ are two square matrices. The eigenvalues of $$AB$$ and $$BA$$ are the same.
Proof: Suppose $$\lambda$$ and $$v$$ are an eigenvalue and the corresponding eigenvector for $$AB$$, so that $$ABv = \lambda v$$. Let $$q = Bv$$. Then $$Aq = \lambda v$$, so $$BAq = \lambda Bv = \lambda q$$. So $$\lambda$$ is also an eigenvalue of $$BA$$, and its associated eigenvector is $$q = Bv$$.