Geodesic
On the ranks of principal submatrices of diagonalizable matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 42-44 Cet article a éte moissonné depuis la source Math-Net.Ru

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As is well known, the rank of a diagonalizable complex matrix can be characterized as the maximum order of the nonzero principal minors of this matrix. The standard proof of this fact is based on representing the coefficients of the characteristic polynomial as the (alternating) sums of all the principal minors of appropriate order. We show that in the case of normal matrices, one can give a simple direct proof, not relying on those representations. Bibl. – 2 titles. 
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Kh. D. Ikramov. On the ranks of principal submatrices of diagonalizable matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 42-44. http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a4/

[1] I. V. Proskuryakov, Sbornik zadach po lineinoi algebre, Nauka, M., 1970

[2] Kh. D. Ikramov, Zadachnik po lineinoi algebre, Lan, SPb., 2006