Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

$B = A + ee^T$.

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

share|cite|improve this question
Suppose $x \in \operatorname{null}(B)$, i.e., $Bx = 0$. What can you prove about $Ax$? – Jonathan Christensen Dec 6 '12 at 21:54
We somehow have to prove that x satisfies Ax = 0, and thereby prove that x belongs to null(A) too? – Ashwin Dec 6 '12 at 22:09

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.