Geodesic
Reducing Complex Matrices to Condensed Forms by Unitary Congruence Transformations
Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 550-559.

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We show that any $n\times n$ conjugate-normal matrix can be brought by a unitary congruence transformation to block-tridiagonal form with the orders of the consecutive diagonal blocks not exceeding $1,2,3,\ldots$, respectively. The proof is constructive; namely, a finite process is described that implements the reduction to the desired form. Sufficient conditions are indicated for the orders of the diagonal blocks to stabilize. In this case, the condensed form is a band matrix.
Keywords: Hermitian matrix, unitary congruence transformation, block-tridiagonal form, Krylov subspace.
Mots-clés : conjugate-normal matrix, Hessenberg form 
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Kh. D. Ikramov. Reducing Complex Matrices to Condensed Forms by Unitary Congruence Transformations. Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 550-559. http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a9/

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