ABSTRACT
Matrix notation and large portions of the theory of linear algebra are used in many areas of the theory of statistics. One notable example is linear model theory. This being the case, it is certainly natural to expect that linear algebraic computational methods will be employed in statistical computing. To be more specific, various numerical methods for transforming a given matrix into some desirable form will be presented. These methods form the basis for several widely used numerical algorithms in statistical computing, and they rank high among the most satisfactory numerical methods in all areas of computing when numerical stability and efficiency are criteria used to make comparisons. A modification of the classical Gram-Schmidt vector orthogonalization process is sometimes used instead of Householder or Givens transformations for certain matrix applications. One of the most numerically stable and generally satisfactory methods in the area of matrix computations is the singular-value decomposition method.
