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My purpose with this post is to know if the following inequality is true or false: $$||S_n^{-1} x_1 x_1^T a_1 + ... + S_n^{-1} x_n x_n^T a_n|| \le x_1^T S_n^{-1} x_1 ||a_1|| + ... + x_n^T S_n^{-1} x_n ||a_n||$$ where $x_1,...x_n,a_1,...,a_n$ are $p$-component (real column) vectors, $S_n = x_1 x_1^T + ... + x_n x_n^T$ is nonsingular for some $n$ and $||\; . \, ||$ a suitable vector norm.

Thanks.

Nick A. P.
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  • Please formulate a correct question. – Mårten W Feb 07 '13 at 08:37
  • The formulation is correct. Is this inequality true or false? If it is false, do you have any counter-example? – Nick A. P. Feb 08 '13 at 19:57
  • It is formulated as a statement followed by a question mark, not as a question. Until you posted the comment above, there was no information about what you wanted to be done with it. Please consider clarifying the original post. – Mårten W Feb 08 '13 at 23:07

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