The similarity class of a matrix

Inverse matrix eigenvalue problems

“…Note that a problem that is formally similar to the (An, AL2)-problem was solved in the recent paper [19]. Since the block Re is square and not the block R1, this problem can be regarded as the (An, A12)-problem only for an even n and l = n/2.…”

“…In reality, the problem considered iLL [19] is motivated by the following observation: if an n x n inatrix T that is silnilar to this matrix, or, more A is not scalar, then we can find a nmtrix B with the first row %, generally, with tile first row where the only constraint is (xn # 0. This assertion can be easily proved with the aid of elementary transformations of rows and columns of A. Theorem 5.7 has arisen as an attempt to generalize the indicated observation from the case l = 1 to greater values of l.…”

Exterior numerical radii and antiinvariant subspaces

“…The author would like to thank Pei Yuan Wu for providing him the references [4] and [8], and Chi-Kwong Li for providing a proof of Theorem 4. Thanks are also due to the referees for some inspiring questions and comments.…”

“…An equivalent matrix version of the latter result (in fact, a stronger result) can be found in the recent work of Hu and Spiegel [4,Theorem 11. In the papers [4] and [8] matrices over a (infinite) field are considered, and their methods of proofs are essentially matrix-theoretic. In contrast, our proofs are geometric, rely on the existence of a Jordan bais of A (as in [4], in case the field is algebraically closed), and can be readily adapted to the most important case (crucial for the development of [4]) when the underlying vector space is over an algebraically closed field.…”