Question

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

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

Answer 1

The correct option is B If A is real symmetric, the eigen values of A are always real and positive

$\therefore$ Eigen values of real symmetric matrix may be -ve also.