Question

The matrix \[ A= \begin{bmatrix} 1 & 1+i & 2i 1-i & 3 & 4 -2i & 4 & 5 \end{bmatrix} \] has

• A. only real eigen values
• B. eigen values of the form \(a+ib,\; a\neq0,\; b\neq0\)
• C. eigen values of the form \(x+iy,\; x=0\)
• D. no inverse

Hint:

For complex matrices, \[ \boxed{ A=A^{H} \Longrightarrow \text{All eigen values are real.} } \] This is one of the most important properties of Hermitian matrices.

Answer 1

The Correct Option is A