Incidence Matrices of Subsets—A Rank Formula

A new rank formula for idempotent matrices with applications

A complex square matrix A is said to be idempotent, or a projector, whenever A2 = A; when A is idempotent, and Hermitian (or real symmetric), it is often called an orthogonal projector, otherwise an oblique projector. Projectors are closely linked to generalized inverses of matrices. For example, for a given matrix A the product PA = AA + is well known as the orthogonal projector on the range (...

On the rank of incidence matrices in projective Hjelmslev spaces

On higher rank numerical hulls of normal matrices

‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...

Some rank equalities for finitely many tripotent matrices

‎A rank equality is established for the sum of finitely many tripotent matrices via elementary block matrix operations‎. ‎Moreover‎, ‎by using this equality and Theorems 8 and 10 in [Chen M‎. ‎and et al‎. ‎On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications‎, ‎The Scientific World Journal 2014 (2014)‎, ‎Article ID 702413‎, ‎7 page...

Quantized Rank R Matrices

First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized n × r matrices as well as certain quantized factor algebras M q (n) of Mq(n) are analyzed. For r = 1, . . . , n − 1, M q (n) is the quantized function algebra of rank r matrices obtained by working modulo the ideal generated by all (r+1)×(r+1) quantum subdeterminants and a certai...