Eigenvalues and Eigenvectors

  • Kenneth Lange
Part of the Statistics and Computing book series (SCO)


Finding the eigenvalues and eigenvectors of a symmetric matrix is one of the basic tasks of computational statistics. For instance, in principal components analysis [13], a random m-vector X with covariance matrix Ω is postulated.


Symmetric Matrix Diagonal Entry Symmetric Matrice Cluster Point Rayleigh Quotient 
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  1. 1.
    Ciarlet PG (1989) Introduction to Numerical Linear Algebra and Optimization. Cambridge University Press, CambridgeGoogle Scholar
  2. 2.
    Demmel JW (1997) Applied Numerical Linear Algebra. SIAM, PhiladelphiaMATHGoogle Scholar
  3. 3.
    Gilbert GT (1991) Positive definite matrices and Sylvester’s criterion. Amer Math Monthly 98:44-46MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Golub GH, Van Loan CF (1996) Matrix Computations, 3rd ed. Johns Hopkins University Press, BaltimoreMATHGoogle Scholar
  5. 5.
    Hämmerlin G, Hoffmann KH (1991) Numerical Mathematics. Springer, New YorkGoogle Scholar
  6. 6.
    Hestenes MR (1981) Optimization Theory: The Finite Dimensional Case. Robert E Krieger Publishing, Huntington, NYGoogle Scholar
  7. 7.
    Hestenes MR, Karush WE (1951) A method of gradients for the calculation of the characteristic roots and vectors of a real symmetric matrix. J Res Nat Bur Standards, 47:471-478MathSciNetGoogle Scholar
  8. 8.
    Isaacson E, Keller HB (1966) Analysis of Numerical Methods. Wiley, New YorkMATHGoogle Scholar
  9. 9.
    Olkin I (1985) A probabilistic proof of a theorem of Schur. Amer Math Monthly 92:50-51MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Ortega JM (1990) Numerical Analysis: A Second Course. SIAM, PhiladelphiaMATHGoogle Scholar
  11. 11.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. Cambridge University Press, CambridgeGoogle Scholar
  12. 12.
    Reiter C (1990) Easy algorithms for finding eigenvalues. Math Magazine. 63:173-178MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Rao CR (1973) Linear Statistical Inference and its Applications, 2nd ed. Wiley, New YorkMATHGoogle Scholar
  14. 14.
    Süli E, Mayers D (2003) An Introduction to Numerical Analysis. Cambridge University Press, CambridgeMATHGoogle Scholar
  15. 15.
    Thisted RA (1988) Elements of Statistical Computing. Chapman & Hall, New YorkMATHGoogle Scholar
  16. 16.
    Trefethen LN, Bau D III (1997) Numerical Linear Algebra. SIAM, PhiladelphiaMATHGoogle Scholar

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© Springer New York 2010

Authors and Affiliations

  1. 1.Departments of Biomathematics, Human Genetics, and Statistics David Geffen School of MedicineUniversity of California, Los AngelesLos AngelesUSA

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