Anti-diagonals of symmetric and skew symmetric matrices with prescribed eigenvalues

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Abstract

The complete relationship between the kth anti-diagonals and the eigenvalues of an n×n (k≤n) real symmetric matrix is obtained. When k is even, the relationship is weak majorization. The Hermitian case is also studied. Similar results are obtained for real and complex skew symmetric matrices. © 2012 Elsevier Inc. All rights reserved.

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Yan, W., & Tam, T. Y. (2013). Anti-diagonals of symmetric and skew symmetric matrices with prescribed eigenvalues. Linear Algebra and Its Applications, 438(3), 1446–1453. https://doi.org/10.1016/j.laa.2012.08.038

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