Canonical angles and limits of sequences of EP and co-EP matrices

Abstract

Canonical angles and limits of sequences of EP and co-EP matricesJulio Benítez * Vladimir Rakočević † AbstractLet A be a square complex matrix. Let P be one of the following properties: a) A is an EP matrix, b) the column space of A is complementary to the column space of A * , and c) the orthogonal complement of the column space of A is the column space of A * . We study the canonical angles between the column space of A and the column space of A * when A satisfies property P. Also, we research the following problem: Let {A m } ∞ m=1 be a sequence of matrices satisfying property P that converges to some matrix A. When does A satisfy property P?

Co-EP Banach algebra elements

“…In this section co-EP Banach algebra elements and Banach space operators will be characterized. Co-EP matrices were studied in [2,4] and co-EP C * -algebra elements in [3]. However, in order to characterize co-EP elements, some preparation is needed.…”

“…The main object of this work is to study a complementary class of object, the co-EP Banach algebra elements, i.e., the Moore-Penrose invertible elements a ∈ A such that aa † − a † a is nonsingular, where A is a Banach algebra, a ∈ A and a † denotes the Moore-Penrose inverse of a. This class of objects were studied for matrices ( [2,4]), for C * -algebras ( [3]) and for rings ( [5]). In section 2, co-EP Banach algebra elements will be characterized.…”

“…Given a unital Banach algebra A, the set of all co-EP elements of A will be denoted by A EP co . Co-EP elements have been studied in [2,3,4].…”

Co-EP-Ness and EP-Ness Involving the Inverse along an Element

“…This invertibility was also considered in [12]. More results about co-EP properties can be seen in [8,10,[14][15][16][17].…”

Two New Matrix Classes Related to the CMP Inverse: CMP and Co-CMP Matrices

“…Significantly, the definition of the co-EP matrices is complementary with that of the EP matrices, i.e., A ∈ C n×n is an EP matrix if AA † = A † A. More information about the co-EP matrices can been seen in [14][15][16][17]. Recently, we [18]…”