real symmetric matrix

Consider a $$3 \times 3$$ real symmetric matrix $$S$$ such that two of its eigen values are $$a \ne 0,$$ $$b\,\, \ne 0$$ with respective eigen vectors $$\left[ {\matrix{ {{x_1}} \c...

Eigen values of a real symmetric matrix are always

If a square matrix $$A$$ is real and symmetric then the eigen values