Suppose \(\mathbb{K}\) is either \(\mathbb{C}\) or \(\mathbb{R}\), \(x,y\in \mathbb{K}^N\) and \(s\le N\). Then the s-term approximation error satisfies

\[ \lvert \sigma_s(x)_1-\sigma_s(y)_1\rvert\le \lVert x-y\rVert_1. \]

[1, Lemma 1.14]

References Link to heading

1. I. Veselic. Class Lecture, Topic: Compressive Sensing. Technische Universität Dortmund, 2017.