Let $K=AA'$ where $A'$ is the transpose of $A$. $A$ is non-singular. Prove that $K\gt0$, or that all elements in $K$ are strictly non-zero. Not sure where to begin with this. I know that if $A$ is non-singular (invertible), its transpose is also invertible, however I'm not sure where the condition of strictly positive is coming from.
2026-04-08 12:30:47.1775651447
Non-singular matrices - properties
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Counterexample, to the question as stated:
Take $$ A = \pmatrix{1&-1\\0&1}\\ AA' = \pmatrix{2&-1\\-1&1} $$