The symmetric eigenvalue problem

In the following, we will be looking for the solutions of the symmetric eigenvalue problem (Golub and Van Loan 2013): \[\begin{equation} \require{physics} \vb{A} \vb{x} = \lambda \vb{x} \thinspace , \end{equation}\] with \(\vb{A} \in \mathbb{R}^{n \times n}\) and \(\vb{A}\) symmetric: \[\begin{equation} \vb{A}^\text{T} = \vb{A} \thinspace . \end{equation}\]

References

Golub, Gene H., and Charles F. Van Loan. 2013. Matrix Computations. Johns Hopkins University Press.