# Matrix product constraints by projection methods

arXiv: https://arxiv.org/abs/1601.01003 · HTML: https://mlsanity.com/paper/1601.01003/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2016.

## Built on by (most cited first, 1 of 1)

- [Avoiding Traps in Nonconvex Problems](https://mlsanity.com/paper/2106.05206/) (2021)

## Abstract (arXiv)

The decomposition of a matrix, as a product of factors with particular properties, is a much used tool in numerical analysis. Here we develop methods for decomposing a matrix C into a product X Y, where the factors X and Y are required to minimize their distance from an arbitrary pair X0 and Y0. This type of decomposition, a projection to a matrix product constraint, in combination with projections that impose structural properties on X and Y, forms the basis of a general method of decomposing a matrix into factors with specified properties. Results are presented for the application of these methods to a number of hard problems in exact factorization.