Geodesic
Reachability of condensed forms via unitary congruence transformations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 8, pp. 1339-1343 Cet article a éte moissonné depuis la source Math-Net.Ru

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There are several well-known facts about unitary similarity transformations of complex $n$-by-$n$ matrices: every matrix of order $n=3$ can be brought to tridiagonal form by a unitary similarity transformation; if $n\ge5$, then there exist matrices that cannot be brought to tridiagonal form by a unitary similarity transformation; for any fixed set of positions (pattern) $S$ whose cardinality exceeds $n(n-1)/2$, there exists an $n$-by-$n$ matrix $A$ such that none of the matrices that are unitarily similar to $A$ can have zeros in all of the positions in $S$. It is shown that analogous facts are valid if unitary similarity transformations are replaced by unitary congruence ones. 
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M. Ghasemi Kamalvand; Kh. D. Ikramov. Reachability of condensed forms via unitary congruence transformations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 8, pp. 1339-1343. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_8_a0/

[1] Longstaff W. E., “On tridiagonalization of matrices”, Linear Algebra Appl., 109 (1988), 153–163 | DOI | MR | Zbl

[2] Fong C. K., Wu P. Y., “Band-diagonal operators”, Linear Algebra Appl., 248 (1996), 185–204 | DOI | MR | Zbl

[3] Pati V., “Unitary tridiagonalization in $M_4(\mathbb C)$”, Proc. Indian Acad. Sci. (Math. Sci.), 111 (2001), 381–397 | DOI | MR | Zbl

[4] Davidson K. R., Djoković D. Ž., “Tridiagonal forms in low dimensions”, Linear Algebra Appl., 407 (2005), 169–188 | DOI | MR | Zbl

[5] Djoković D. Ž., MacDonald M. L., “Orthogonal invariants of a matrix of order four and applications”, J. Pure Appl. Algebra, 202 (2005), 259–283 | DOI | MR | Zbl

[6] Djoković D. Ž., Johnson C. R., “Unitarily achievable zero patterns and traces of words in $A$ and $A^*$”, Linear Algebra Appl., 421 (2007), 63–68 | DOI | MR | Zbl

[7] Fassbender H., Ikramov Kh. D., “Some observations on the Youla form and conjugate normal matrices”, Linear Algebra Appl., 422 (2007), 29–38 | DOI | MR | Zbl

[8] Milnor Dzh., Uolles A., Differentsialnaya topologiya. Nachalnyi kurs, Mir, M., 1972 | MR | Zbl

[9] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989 | MR

[10] Bunse-Gerstner A., Stöver R., “On a conjugate gradient-type method for solving complex symmetric linear systems”, Linear Algebra Appl., 287 (1999), 105–123 | DOI | MR | Zbl