Shorted Matrices - An Extended Concept and Some Applications in Design and Analysis of Experiments.
INDIANA UNIV AT BLOOMINGTON DEPT OF MATHEMATICS
Pagination or Media Count:
The concept of a shorted operator on the cone C sub n of nonnegative definite matrices of order n x n introduced by Krein and studied recently by Anderson and Trapp is extended to a wider class of matrices. For matrices in C sub n, the shorting operation is permissible with reference to any subspace S of the n dimensional Euclidean space E to the nth power, provided restrictions are symmetrically placed on the row and column spans. For general matrices, the shorting operation is uniquely defined if and only if certain conditions are satisfied by the matrix itself and by subspaces providing restrictions on the row and column spans. The key point in this development is a theorem of Anderson and Trapp which exhibits the shorted n.n.d. matrix as the limit of a sequence of parallel sum operators. Some applications of the shorted operator in mathematical statistics with special reference to the design and analysis of experiments are provided.
- Theoretical Mathematics