Gram-Schmidt process is a way to convert a set of non-orthogonal vectors into a set of orthogonal vectors, while preserving the subspaces spanned by initial vectors. Gram-Schmidt process in Euclidean spaces is captured in a computational algorithm called QR-decomposition.

QR-decomposition is used in many computational algorithms as an intermediate step, most notably, in calculating eigenvalues of matrices (the QR-algorithm).

In the context of statistics, Gram-Schmidt process and QR-algorithm have many applications:

- A proof that Studentized means have Student t-distribution.
- Solution of least squares problems.
- Construction of orthogonal contraststs, such as orthogonal polynomial contrasts.

The attached documents contain an exposition of Gram-Schmidt process, QR-decomposition and a statistical application to Studentized means.

Attachment | Size |
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A tutorial on Gram-Schmidt and QR-decomposition in PDF format | 106.09 KB |

The TeXmacs source of the above document | 24.73 KB |

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