Beresford Parlett’s The Symmetric Eigenvalue Problem is widely considered "the bible" for those working with matrix computations. Originally published in 1980 and later reprinted by SIAM in its Classics in Applied Mathematics series, the book is celebrated for its lively commentary and authoritative "art of computing" perspective.
The Soul of a Matrix: Why Parlett’s "Symmetric Eigenvalue Problem" is Still Must-Read parlett the symmetric eigenvalue problem pdf
Focus on Symmetric Case
By restricting to symmetric (or Hermitian) matrices, Parlett exploits spectral properties (real eigenvalues, orthogonal eigenvectors) to present cleaner, more powerful theory and stable algorithms. This specialization makes the book uniquely authoritative. This specialization makes the book uniquely authoritative
: Covers techniques for approximating eigenvalues in more complex contexts, such as Lanczos algorithms , subspace iteration, and Krylov subspaces. SIAM Publications Library Summary of Topics Covered Fundamental Theory such as Lanczos algorithms
The Symmetric Eigenvalue Problem | SIAM Publications Library