# Low-rank Approximation of Linear Maps

arXiv: https://arxiv.org/abs/1812.09042 · HTML: https://mlsanity.com/paper/1812.09042/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2018.

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

- [State-Of-The-Art Algorithms For Low-Rank Dynamic Mode Decomposition](https://mlsanity.com/paper/2108.09160/) (2021)

## Abstract (arXiv)

This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results obtained in the finite dimensional case for the Frobenius norm. The theorem provides the basis for the design of tractable algorithms for kernel or continuous DMD.