1. Summability Methods on Matrix Spaces
- Author
-
Josephine Mitchell
- Subjects
Combinatorial analysis ,Pure mathematics ,Matrix (mathematics) ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,Matrix analysis ,0101 mathematics ,01 natural sciences ,Complex number ,Potential theory ,Mathematics - Abstract
The matrix spaces under consideration are the four main types of irreducible bounded symmetric domains given by Cartan (5). Let z = (zjk) be a matrix of complex numbers, z' its transpose, z* its conjugate transpose and I = I(n) the identity matrix of order n. Then the first three types are defined by(1)where z is an n by m matrix (n ≤ m), a symmetric or a skew-symmetric matrix of order n (16). The fourth type is the set of complex spheres satisfying(2)where z is an n by 1 matrix. It is known that each of these domains possesses a distinguished boundary B which in the first three cases is given by(3)(In the case of skew symmetric matrices the distinguished boundary is given by (2) only if n is even.)
- Published
- 1961