Geodesic
On tridiagonal conjugate-normal matrices
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 179-185

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Conjugate-normal matrices play the same role in the theory of unitary congruences as conventional normal matrices do with respect to unitary similarities. Naturally, the properties of both matrix classes are fairly similar up to the distinction between the congruence and similarity. However, in certain respects, conjugate-normal matrices differ substantially from normal ones. Our goal in this paper is to indicate one of such distinctions. It is shown that none of the familiar characterizations of normal matrices having the irreducible tridiagonal form has a natural counterpart in the case of conjugate-normal matrices. 
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     title = {On tridiagonal conjugate-normal matrices},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a0/}
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Kh. D. Ikramov. On tridiagonal conjugate-normal matrices. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 179-185. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a0/