TIFR ECE 2013 | Question: 12

Question

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

• A. the same eigenvalues as of $A$ but different eigenvectors
• B. the same eigenvalues and eigenvectors as of $A$
• C. the eigenvalues smaller than those of $A$ and same eigenvectors as of $A$
• D. eigenvalues and eigenvectors with no relation to those of $A$
• E. None of the above