On pairs of matrices that satisfy certain polynomial identities
✍ Scribed by Henrique F. da Cruz; Rosário Fernandes
- Book ID
- 113772132
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 313 KB
- Volume
- 436
- Category
- Article
- ISSN
- 0024-3795
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It is proved that Jordan pairs P(n, m) = (Mn. m, Mm,. ) of n X m matrices over a field k are distinguished up to embedding by means of polynomial identities. Also, a basis of identities of P(1, n), where n can be infinite and the characteristic of k is equal to zero, is found. © Elsevier Science Inc
A pair of m × n matrices (A, B) is said to be rank-sum-maximal if ρ(A + B) = ρ(A) + ρ(B), and rank-sum-minimal if ρ(A + B) = |ρ(A)ρ(B)|. We characterize the linear operators preserving the set of rank-sum-maximal pairs over any field and the linear operators preserving the set of rank-sum-minimal pa