Question

If $A$ is square symmetric real values matrix of dimensions $2n$, then the eigen values of $A$ are

• A. $2n$ distinct real values
• B. $2n$ real values not necessrily distinct
• C. $n$ distinct paris of complex conjugate numbers
• D. $n$ pairs of complex conjugate numbers, not necessarily distinct

Answer 1

The correct option is B $2n$ real values not necessrily distinct

We know that the number of eigen values of $A_{n\times n}$ is $n$ and eigen values of real symmetric matrix are always real.
Hence for real symmetric matrix $A_{2n\times 2n}$ there must exist $2n$ real eigen values which may or may not be repeated.