MAHLER MATRICES AND THE EQUATION QA = AQM
Abstract
Several sets of matrices are defined; each set forms an abelian group. The elements of the matrices are 0, 1, -1 and other roots of unity (or sums of roots of unity). The determinant, characteristic roots, vectors, and elementary divisors are also found. Thus the matrices form a convenient set of test matrices for a routine which purports to solve a matrix. A typical test matrix may involve nonreal elements; if each element of the matrix is replaced by a 2 by 2 matrix in the usual way the roots of the expanded real matrix are the roots of the test matrix and their conjugates. The vectors of the expanded matrix are easily found also. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1961
- Accession Number
- AD0261914
Entities
People
- J.l. Brenner
Organizations
- University of Wisconsin–Madison