A basic decomposition result related to the notion of the rank of a matrix and applications.
Mortici, Cristinel (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Similarity:
Mortici, Cristinel (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Similarity:
Miroslav Fiedler (2003)
Mathematica Bohemica
Similarity:
We present some results on generalized inverses and their application to generalizations of the Sherman-Morrison-Woodbury-type formulae.
Chao Ma (2017)
Open Mathematics
Similarity:
Let x, y be two distinct real numbers. An {x, y}-matrix is a matrix whose entries are either x or y. We determine the possible numbers of x’s in an {x, y}-matrix with a given rank. Our proof is constructive.
Duanmei Zhou, Guoliang Chen, Jiu Ding (2017)
Open Mathematics
Similarity:
Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.
Seok-Zun Song, Young-Bae Jun (2006)
Discussiones Mathematicae - General Algebra and Applications
Similarity:
The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.
Cao, Chongguang, Tang, Xiaomin (2004)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Štefan Schwarz (1985)
Mathematica Slovaca
Similarity:
Yong Ge Tian, George P. H. Styan (2002)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
It is shown that where is idempotent, has full row rank and . Some applications of the rank formula to generalized inverses of matrices are also presented.
Berman, Avi, Friedland, Shmuel, Hogben, Leslie, Rothblum, Uriel G., Shader, Bryan (2008)
The Electronic Journal of Combinatorics [electronic only]
Similarity: