I found that for a positive definite matrix $Q$ and a square matrix $A$, if $A^TQA<Q$, then $\rho(A)<1$. But what if $\sum_{i=1}^pA_i^TQA<Q$? can we get $\rho(\sum_{i=1}^pA_i^TA)<1$?
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What do you mean by $\rho(A)$? – Arin Chaudhuri Sep 24 '16 at 02:09
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$\rho(A)$ means the spectral radius of matrix A – Jin Sep 24 '16 at 02:39
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And what do you mean by $A < B$ for matrices $A$ and $B$? – Arin Chaudhuri Sep 24 '16 at 14:34
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It means that $B-A$ is positive definite. – Jin Sep 26 '16 at 01:00