Geodesic
On normal matrices with normal principal submatrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XI, Tome 229 (1995), pp. 63-94

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Let A be a normal $n\times n$ matrix. This paper discusses in detail under what conditions and in what way $A$ can be dilated to a normal matrix of order $n+1$ or $n+2$. Bibliography: 4 titles. 
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     author = {Kh. D. Ikramov and L. \'El'zner},
     title = {On normal matrices with normal principal submatrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {63--94},
     publisher = {mathdoc},
     volume = {229},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_229_a2/}
}
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Kh. D. Ikramov; L. Él'zner. On normal matrices with normal principal submatrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XI, Tome 229 (1995), pp. 63-94. http://geodesic.mathdoc.fr/item/ZNSL_1995_229_a2/