Details on the computation of the eigenvalue and singular value decompositions are presented at length in Stewart (2001) and more briefly in Chapters 7 and 8 of Golub & Van Loan (1996). A classic reference on the particulars of the symmetric case is Parlett (1980), while Trefethen & Embree (2005) focuses on the non-normal case. Dimension reduction via the SVD often goes by the name principal component analysis, which is the subject of Jolliffe (2002).
- Stewart, G. W. (2001). Matrix Algorithms Volume 2: Eigensystems. SIAM.
- Golub, G. H., & Van Loan, C. F. (1996). Matrix Computations (3rd ed.). JHU Press.
- Parlett, B. N. (1980). The Symmetric Eigenvalue Problem. SIAM.
- Trefethen, L. N., & Embree, M. (2005). Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press.
- Jolliffe, I. T. (2002). Principal Component Analysis (Second). Springer Science & Business Media.