On normal EPr matrices.
نویسندگان
چکیده
منابع مشابه
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The rank subtractivity partial ordering is defined on Cn×n (n ≥ 2) by A ≤− B⇔ rank(B−A) = rankB− rankA, and the star partial ordering by A ≤∗ B⇔ A∗A = A∗B ∧ AA∗ = BA∗. If A and B are normal, we characterize A ≤− B. We also show that then A ≤− B ∧ AB = BA⇔ A ≤∗ B⇔ A ≤− B ∧ A ≤− B. Finally, we remark that some of our results follow from well-known results on EP matrices.
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It would be correct to add that the main contribution of [2] was to prove, for arbitrary n, the necessity of some equalities for the entries of a normal Toeplitz matrix of order n. These equalities are in fact equivalent to the authors’ equations (1) in the real case. The full solution of the problem (of describing normal Toeplitz matrices) for the real case was given in [3]. The same year anot...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1961
ISSN: 0026-2285
DOI: 10.1307/mmj/1028998512