Updates from Overleaf

Author: japm48

main.tex

@@ -891,7 +891,7 @@
 
     \item Each entry $(A\transp A)_{ij}$ is the inner product of two columns of $A$ (for $AA\transp$, those are rows of $A$). 
     
-    This clearly explains why for $Q$ with $m=n$ orthonormal columns we get $ Q\transp Q=QQ\transp=I$; that is, $Q$ is orthogonal.
+    This clearly explains why for $Q$ orthogonal with $m=n$ orthonormal columns we get $ Q\transp Q=QQ\transp=I$; that is, $Q$ is .
     
     Note that $Q$ here is square; if it was $\hat Q$ rectangular (i.e.\@ \emph{semi}-orthogonal, with orthonormal columns; requires $m\ge n$), then the product $\hat Q\transp \hat Q = I$ is never commutative (the resulting matrix has a different size!); in fact, $\hat{Q}\hat{Q}\transp$ is NOT full rank (nonetheless, it is still SPSD).