Maximum number of Q-orthogonal vectors

linear-algebra convex-optimization symmetric-matrices vectors positive-definite

Solution 1:

and I guess that if there are n Q-orthogonal vectors that are linearly independent, then Q must be positive definite.

This statement is false. Consider the case $Q = 0$. Then every pair of vectors is $Q$-orthogonal and so clearly there exists $n$ linearly independent $Q$-orthogonal vectors but $Q$ is not positive definite.

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