# sprank

## Purpose

Sparse matrix structural rank.

## Synopsis

    r = sprank(A)

## Description

`r = sprank(A)` is the structural rank of the matrix `A`. This is also known as maximum traversal, maximum assignment, and size of a maximum matching in the graph of `A`.

It is always true that `sprank(A) >= rank(A)`.

Furthermore, in exact arithmetic

    sprank(A) == rank(sprand(A))

with probability one.

## Examples

The 3-by-3 matrix

    A = [ 2    0    1
          0    0    0
          3    0    x ]

has `sprank(A)` `=` `2` for any value of `x`. It also has `rank(A)` `=` `2`, unless `x` `=` `3/2` in which case, `rank(A) = 1`.

## See Also

    dmperm, rank

(c) Copyright 1994 by The MathWorks, Inc.