A simple question. Why is the sum of the singular values of a matrix called its nuclear norm? What is the origin of, and motivation for, this term?
Apparently the term nucleus is sometimes used to refer to the kernel of a linear transformation, but that doesn't seem to have anything to do with singular values.
To save you the effort, neither nucleus nor nuclear have entries in Earliest Known Uses of Some of the Words of Mathematics.
Mariano explains in a comment that the nuclear norm is related to the norm of nuclear operators, which in turn get their name because they generalize operators given by kernels.
There is a lot more information on nuclear operators at the Encyclopedia of Mathematics.