When I want to calculate eigenvectors of the following matrix in Mathematica the only answer it gives me is zero vector, anybody knows how to fix this? here's my matrix : \begin{equation} X=\left(\begin{array}{cccc} 0 & 1 & 0 & 0&0&0\\ 1 & 0 & \sqrt{2} & 0&0&0\\ 0 & \sqrt{2} & 0 & \sqrt{3}&0&0\\ 0 & 0 & \sqrt{3} & 0& \sqrt{4} &0\\0&0&0&\sqrt{4} &0&\sqrt{5} \\ 0&0&0&0&\sqrt{5} &0 \end{array}\right) \end{equation} heres the code:
X = {{0, 1, 0, 0, 0, 0},
{1, 0, Sqrt[2], 0, 0, 0},
{0, Sqrt[2], 0, Sqrt[3], 0, 0},
{0, 0, Sqrt[3], 0, Sqrt[4], 0},
{0, 0, 0, Sqrt[4], 0, Sqrt[5]},
{0, 0, 0, 0, Sqrt[5], 0}
};
Eigenvectors[X]
The point is I don't want to find them numerically I want analytical expression for eigenvectors.
ToRadicals
to make Mathematica expand theRoot
objects into normal-looking numbers. $\endgroup$