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I couldn't find a proof of the algebraic inequality

${\displaystyle \varkappa _{\beta }^{\alpha }\varkappa _{\alpha }^{\beta }\geq {\frac {1}{3}}\left(\varkappa _{\alpha }^{\alpha }\right)^{2}}$

and that's why I tried to prove it myself. I found a partial numerical proof for the general non-symmetric case and a strict symbolic proof for the symmetric case. For the general case, I took the hint from Landau & Lifshitz and diagonalised the matrix. The proof is in the web page [1]. I haven't referenced it in the text because someone may think that I promote my site. This is not my intention.

If someone finds a proof, please include it in the article.Lantonov (talk) 17:37, 17 August 2020 (UTC)[reply]

As an idea, maybe use Cauchy-Schwarz inequality but haven't worked out details yet. Lantonov (talk) 18:30, 17 August 2020 (UTC)[reply]

I found a rigorous proof using the properties of Frobenius norm and Cauchy-Schwarz inequality and changed the web page [2] accordingly.Lantonov (talk) 09:38, 4 April 2024 (UTC)[reply]