Review Note

Last Update: 09/23/2023 03:11 PM

Current Deck: EEN100: Theory and exercises

Published

Fields:

Front
Uniqueness of solution to (P0)
Back
Let \(A \in \mathbb R^{m \times n}\). The following are equivalent
  1. Every \(s\)-sparse \(x \in \mathbb R^n\) is the unique \(s\)-sparse solution of \(Az=Ax\).
  2. \(\mathrm{ker}(A)\) does not contain \(2s\)-sparse vectors (except 0)
  3. Every set of \(2s\) columns of \(A\) is linearly independent

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