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In mathematics, specifically in linear algebra, the spark of a matrix A is the smallest number n such that there exists a set of n columns in A which are linearly dependent. Formally,
By contrast, the rank of a matrix is the smallest number k such that all sets of k + 1 columns in A are linearly dependent.
The concept of the spark is of use in the theory of compressive sensing, where requirements on the spark of the measurement matrix are used to ensure stability and consistency of various estimation techniques.
References
- Donoho, David L.; Elad, Michael (March 4, 2003), "Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization", Proc. Nat. Acad. Sci. 100 (5): 2197–2202, doi:, http://www.pnas.org/cgi/doi/10.1073/pnas.0437847100
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- This page was last modified on 29 December 2008, at 06:58.
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