Opening book details…
Can I read Commuting Pairs and Triples of Matrices and Related Varieties on EtoBox?
Commuting Pairs and Triples of Matrices and Related Varieties by Robert M. Guralnick; B.A. Sethuraman is a Mathematics article available to read on EtoBox.
What is Commuting Pairs and Triples of Matrices and Related Varieties about?
In this note, we show that the set of all commuting d-tuples of commuting n × n matrices that are contained in an n-dimensional commutative algebra is a closed set, and therefore, Gerstenhaber's theorem on commuting pairs of matrices is a consequence of the irreduciblity of the variety of commuting pairs. We show that the variety of commuting triples of 4 × 4 matrices is irreducible. We also study the variety of n-dimensional commutative subalgebras of M n (F ), and show that it is irreducible of dimension n 2n for n 4, but reducible, of dimension greater than n 2n for n 7.
Who reads Commuting Pairs and Triples of Matrices and Related Varieties?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Robert M. Guralnick; B.A. Sethuraman
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0024-3795)
- Published
- 2000
- Language
- EN
- Field
- Mathematics (Physical Sciences)