Cardinality of a vector

The cardinality of a vector is the number of non-zero elements in it. It is sometimes called the -norm of , although the cardinality function is not a norm.

The cardinality is denoted , or .

For example, the vector

has cardinality .

The cardinality function is useful in many problems, however it is difficult to optimize. In cardinality minimization problems, the -norm is often used as a surrogate.