Spark (mathematics)

Spark (mathematics)

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. 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

* Citation
last = Donoho
first = David L.
author-link =
last2 = Elad
first2 = Michael
author2-link =
title = Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization
journal = Proc. Nat. Acad. Sci.
volume = 100
issue = 5
pages = 2197–2202
date = March 4, 2003
url = http://www.pnas.org/cgi/doi/10.1073/pnas.0437847100
doi = 10.1073/pnas.0437847100
id =


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