= Singular obstruction to normalized quantum matrix multiplication
If $|b\rangle$ lies in the <kernel> of $A$, then $A|b\rangle=0$ has no normalized <quantum state>. A request to produce that normalized vector with positive <probability> is consequently undefined. For example, $A=\operatorname{diag}(0,1/2)$ on one <qubit> has distinct dyadic <eigenvalues>, but annihilates $|0\rangle$. The corrected filtering assertion requires $A|b\rangle\neq0$; it cannot be repaired by assigning a positive success probability to this input.
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