Ela the Jordan
نویسنده
چکیده
The relationship between the Jordan forms of the matrix products AB and BA for some given A and B was first described by Harley Flanders in 1951. Their non-zero eigenvalues and non-singular Jordan structures are the same, but their singular Jordan block sizes can differ by 1. We present an elementary proof that owes its simplicity to a novel use of the Weyr characteristic.
منابع مشابه
Ela Jordan Left Derivations in Full and Upper Triangular Matrix Rings
In this paper, left derivations and Jordan left derivations in full and upper triangular matrix rings over unital associative rings are characterized.
متن کاملEla Pseudomonotonicity and Related Properties in Euclidean Jordan Algebras
In this paper, we extend the concept of pseudomonotonicity from Rn to the setting of Euclidean Jordan algebras. We study interconnections between pseudomonotonicity, monotonicity, and the Z-property.
متن کاملInvestigating Teacher Learning and Change in a Professional Learning Community: Integrating ELA and Social Studies Curriculum
......................................................................................................................................... iii Acknowledgements ........................................................................................................................ iv Table of
متن کاملEla Linear Maps Preserving the Idempotency of Jordan Products of Operators
Let B(X ) be the algebra of all bounded linear operators on a complex Banach space X and let I(X ) be the set of non-zero idempotent operators in B(X ). A surjective map φ : B(X ) → B(X ) preserves nonzero idempotency of the Jordan products of two operators if for every pair A, B ∈ B(X ), the relation AB + BA ∈ I(X ) implies φ(A)φ(B) + φ(B)φ(A) ∈ I(X ). In this paper, the structures of linear s...
متن کاملEla Norm Preservers of Jordan Products
Norm preserver maps of Jordan product on the algebra Mn of n×n complex matrices are studied, with respect to various norms. A description of such surjective maps with respect to the Frobenius norm is obtained: Up to a suitable scaling and unitary similarity, they are given by one of the four standard maps (identity, transposition, complex conjugation, and conjugate transposition) on Mn, except ...
متن کامل