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What are some measurements of the sparseness of a matrix, which are often used? Thanks!

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The sparsity of a matrix is most commonly defined as the number of nonzero elements divided by the total number of elements. Say $A$ is $m\times n$; then the sparsity of $A$ is

$$ \frac{\#\{a_{ij}:a_{ij}\neq 0\}}{n\cdot m} $$

There are many different measures of sparsity in signal processing, however, all of which relate to different notions of compressibility and spectrum. See this article for a thorough discussion of many of them.

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