
05701694
j
2010b.00512
Sj\"odin, Tord
The GramSchmidt algorithm for a general angle. (GramSchmidt's algoritm f\"or en allm\"an vinkel.)
Normat. 57, No. 4, 173179 (2009).
2009
Nationellt Centrum f\"or Matematikutbildning (NCM), G\"oteborgs Universitet, G\"oteborg
SV
H65
linear algebra
orthogonalization
generalization
Summary: The classical GramSchmidt algorithm allows you to exhibit an orthogonal basis with respect to a positive definite form (the normalization that each basis element has length one is of course trivial). In this paper the question is posed whether it also works when orthogonality is replaced with some other angle $\theta$. The author shows that it is possible if and only if $\frac{1}{n1}<\cos\theta<1$ where $n$ is the dimension of the space.