GATE ECE 2014 Set 3 | Question: 27

Question

Which one of the following statements is NOT true for a square matrix $A$?

• A. If $A$ is upper triangular, the eigenvalues of $A$ are the diagonal elements of it
• B. If $A$ is real symmetric, the eigenvalues of $A$ are always real and positive
• C. If $A$ is real, the eigenvalues of $A$ and $A^{T}$ are always the same
• D. If all the principal minors of $A$ are positive, all the eigenvalues of $A$ are also positive