A necessary and sufficient condition for rank(A -AN(MT AN)-MT A) =rank(A) -rank(AN(MT AN)-MT A)

Authors：张骞; 袁永新

Source：湖北师范学院学报(自然科学版), 2016, 36(1).

DOI：10.3969/j.issn.1009-2714.2016.01.017

• rank equality
• canonical correlation decomposition(CCD)
• full rank decomposition
• generalized inverse

In this paper, by applying the canonical correlation decomposition of the matrix pair and the full rank decomposition of the matrix A, we obtain a necessary and sufficient condition for the validity of the rank subtractivity formula rank(A -AN(MTAN)-MTA) =rank(A) -rank(AN(MTAN) -MTA).

• Institution
  湖北师范学院