0 past simple and past participle of factorize --
1 If you factorize a number, you divide it into factors. --
Intuitively we think that 0 and 1 are simple numbers, and that prime numbers are somehow more complex the numbers may be factorized.
Note that only diagonalizable matrices can be factorized in this way.
A matrix can also be factorized into a product of matrices of special types, for an application in which that form is convenient.
It turns out that all square matrices can be factorized in this form, and the factorization is numerically stable in practice.
However, a form of this sort is a member of a "curved exponential family", which allows multiple factorized terms in the exponent.
For example, these functions can be such that their inverses can be computed only if certain large integers are factorized.
Here, the idea is to use a flat, highly factorized variant of first-order logic with generalized quantifiers as a means for representing analyses from both shallow and deep processing.
Based on the technique of factorized semantics, we provide semantic specifications and correctness proofs for both on-line and off-line partial evaluation of first-order functional programs.
