SJSU Singular Matrix Database

Structural rank, theoretical rank and numerical rank

The structural rank of a matrix is the number of entries in the maximum transversal of the bipartite graph of A. It is also known as the maximum assignment and size of a maximum matching in the bipartite graph of A. The Matlab function sprank calculates the structural rank of a matrix. If we use term "theoretical rank" to represent the rank as used in a theoretical mathematics course then:

Here is a simple example. For some small value ε > 0 let A be the matrix:

  1    1  
1
  0  
  1     1  
1
  0  
  1     1   1 + ε   0  
  0     0  
0
  0