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TIFR ECE 2013 | Question: 12

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Let $A$ be a Hermitian matrix and let $I$ be the Identity matrix with same dimensions as $A$. Then for a scalar $\alpha>0, A+\alpha I$ has

  1. the same eigenvalues as of $A$ but different eigenvectors
  2. the same eigenvalues and eigenvectors as of $A$
  3. the eigenvalues smaller than those of $A$ and same eigenvectors as of $A$
  4. eigenvalues and eigenvectors with no relation to those of $A$
  5. None of the above

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