Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Change of basis and Gram-Schmidt orthonormalization in special
  relativity   While an explicit basis is common in the study of Euclidean spaces, it is
usually implied in the study of inertial relativistic systems. There are some
conceptual advantages to including the basis in the study of special
relativistic systems. A Minkowski metric implies a non-orthonormal basis, and
to deal with this complexity the concepts of reciprocal basis and the vector
dual are introduced. It is shown how the reciprocal basis is related to upper
and lower index coordinate extraction, the metric tensor, change of basis,
projections in non-orthonormal bases, and finally the Gram-Schmidt procedure.
It will be shown that Lorentz transformations can be viewed as change of basis
operations. The Lorentz boost in one spatial dimension will be derived using
the Gram-Schmidt orthonormalization algorithm, and it will be shown how other
Lorentz transformations can be derived using the Gram-Schmidt procedure.

11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas