On the subject of 2x2 matrices.
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Bokuan Li
2026-10-14 16:53:02 -04:00
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@@ -73,7 +73,7 @@ The following is a slight generalisation of one form of the above example, but s
\normn{\phi_n(1_{M_n(A)})}_{M_n(B)}^{-1} &\le \phi_n(1_{M_n(A)})^{-1}
\end{align*}
By the \hyperref[Schur complement condition]{lemma:schur-complement-positive},
By the \hyperref[Schur complement condition]{proposition:schur-complement-positive},
\begin{align*}
\phi_n(1_{M_n(A)}) &\ge \phi_n(T)\phi_n(1_{M_n(A)})^{-1}\phi_n(T)^* \\
&\ge \normn{\phi_n(1_{M_n(A)})}_{M_n(B)}^{-1}\phi_n(T)\phi_n(T)^* \\