Definition_reciprocal_frame.tex

%
% Copyright © 2018 Peeter Joot.  All Rights Reserved.
% Licenced as described in the file LICENSE under the root directory of this GIT repository.
%
\makedefinition{Reciprocal frame}{dfn:reciprocal:frame}{
Given a subspace basis \( \beta = \setlr{ \Bx_1, \Bx_2, \cdots \Bx_m } \), not
necessarily orthonormal, the \textit{reciprocal frame} is the set \( \setlr{ \Bx^1, \Bx^2, \cdots \Bx^m } \in \Span \beta \) satisfying
\begin{equation*}
\Bx_i \cdot \Bx^j = {\delta_i}^j,
\end{equation*}
where the vector \( \Bx^j \) is not the j-th power of \( \Bx \), but is a superscript index, the conventional way of denoting a reciprocal frame vector, and \( {\delta_i}^j \) is the Kronecker delta.
} % definition