sparsity

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Sparsity

We denote the sparsity of a vector $x$ by

| | x | |_{0} := # {i : x_{i} \neq 0} = | {i : x_{i} \neq 0} |

If $| | x | |_{0} \leq k$ , we say that $x$ is $k$ -sparse

Note

This is not a norm; it is not homogeneous.

Review

#flashcards/math/rmt

Why is the sparsity not a norm?
-?-
It is not homogenous

What is the sparsity of a vector (in English)?
-?-
The number of non-zero entries

File	Last Modified
distinguishing is equivalent to double nullspace property	2025-09-11
Random Matrix Lecture 05	2025-09-11

sparsity

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