@article {IOPORT.05015127,
    author       = {Vandebril, Raf and Van Barel, Marc},
    title        = {A note on the nullity theorem.},
    year         = {2006},
    journal      = {Journal of Computational and Applied Mathematics},
    volume       = {189},
    number       = {1-2},
    issn         = {0377-0427},
    pages        = {179-190},
    publisher    = {Elsevier Science B.V. (North-Holland), Amsterdam},
    doi          = {10.1016/j.cam.2005.02.007},
    abstract     = {The nullity of a matrix is the dimension of its right null space. The nullity theorem [cf. {\it M. Fiedler} and {\it T. L. Markham}, Linear Algebra Appl. 74, 225--237 (1986; Zbl 0592.15002)] relates the rank of a subblock of a matrix and an approriate subblock in its inverse. An alternative proof of this theorem is given in terms of determinants. Similar theorems are given, to relate the rank of a subblocks of a matrix and an appropriate subblock in the $L$, $U$, or $Q$ factors in the LU and QR factorization of a matrix. This is very useful to predict the structure of these factorizations and of the inverse of a matrix that has a certain rank structure like being semiseparable, Hessenberg, etc.},
    reviewer     = {Adhemar Bultheel (Leuven)},
    identifier   = {05015127},
}