8.3 Sparse Matrices

Types: N/A
Examples: N/A
Constructions: 8.4 Special Sparsity Notation
Generalizations: N/A

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Sparse Matrices

Let $A \in R^{m \times n}$ . The total number of elements of $A$ is denoted

numel (A) = m \cdot n .

The total number of nonzero elements in $A$ is $nnz (A)$ . To count the number of zero elements, we can calculate

numel (A) - nnz (A) .

We call a matrix sparse if

\frac{nnz (A)}{numel (A)} \leq 0.10 (approximately) .

Remark. Sparse matrices are matrices that have much fewer zeros than you would expect.
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