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
- Every \(s\)-sparse \(x \in \mathbb R^n\) is the unique \(s\)-sparse solution of \(Az=Ax\).
- \(\mathrm{ker}(A)\) does not contain \(2s\)-sparse vectors (except 0)
- Every set of \(2s\) columns of \(A\) is linearly independent
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