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$A$ and $B$ are two symmetric and PSD matrices. Also,

$B = A + ee^T$.

How can one prove that $\operatorname{null}(B) \subset \operatorname{null}(A)$?

  • 1
    Suppose $x \in \operatorname{null}(B)$, i.e., $Bx = 0$. What can you prove about $Ax$?2012-12-06
  • 0
    We somehow have to prove that x satisfies Ax = 0, and thereby prove that x belongs to null(A) too?2012-12-06

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