Jason (jcreed) wrote,
Jason
jcreed

-

First day of classes.

Went to grad algo in the morning. Manuel Blum
is a pretty decent lecturer. Also got suckered
in to sitting in on quantum comp by Pete. Maybe
it'll make a little more sense this time around.
I figured out at least that the definitions
stop being circular once I realized that the bra
vectors are really just the complex linear functionals
on the ket vectors, and that the space of bra vectors
is isomorphic to the space of ket vectors by
a pair of *conjugate-linear* morphisms.

Also the tensor product of V and W is the (iso-unique) space
T with an initial bilinear map f : V x W -> T.
I suppose the categorical product of two spaces has dimension
the sum of their dimensions?
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