Abstract
This paper gives simple proofs of the Sylvester (ℓ = 2) and Frobenius (ℓ = 3) inequalities. Moreover, a new sufficient condition for the equality of the Frobenius inequality is provided. In addition, an extension for ℓ > 3 matrices and an application to generalized inverses are provided.
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Thome, N. Inequalities and equalities for ℓ = 2 (Sylvester), ℓ = 3 (Frobenius), and ℓ > 3 matrices. Aequat. Math. 90, 951–960 (2016). https://doi.org/10.1007/s00010-016-0412-4
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DOI: https://doi.org/10.1007/s00010-016-0412-4