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Displaying similar documents to “On the Rodman-Shalom conjecture regarding the Jordan form of completions of partial upper triangular matrices.”

On the Yang-Baxter-like matrix equation for rank-two matrices

Duanmei Zhou, Guoliang Chen, Jiu Ding (2017)

Open Mathematics

Similarity:

Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.

On a nonnegative irreducible matrix that is similar to a positive matrix

Raphael Loewy (2012)

Open Mathematics

Similarity:

Let A be an n×n irreducible nonnegative (elementwise) matrix. Borobia and Moro raised the following question: Suppose that every diagonal of A contains a positive entry. Is A similar to a positive matrix? We give an affirmative answer in the case n = 4.