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jason
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sum of positive definite matrix

sum of positive definite matrix $A+B $is positive definite. I want to look at the spectrum of $C=A+B$

can we say the ith largest eigenvalue of $C$ is no less than the ith largest eigenvalue of $A$ i.e. $B$ as positive definite matrix, has contribution to the growth of spectrum?

jason
  • 553
  • 3
  • 13