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

$B = A + ee^T$.

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

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    We somehow have to prove that x satisfies$Ax$= 0, and thereby prove that x belongs to null(A) too?2012-12-06

1 Answers 1

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Hint: look at $x^tBx=x^tAx+x^tee^tx$, where $x$ is such that $Bx=0$.