nchairx (8aug21)

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+% \iffalse meta-comment
+%
+% Copyright (C) 2018 - 2021 by ChairX
+%
+% This file may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either
+% version 1.3 of this license or (at your option) any later
+% version.  The latest version of this license is in:
+%
+%    http://www.latex-project.org/lppl.txt
+%
+% and version 1.3 or later is part of all distributions of
+% LaTeX version 2005/12/01 or later.
+%
+% This file contains the documentation of all linear algebra related macros .
+%
+% Macros have to be described by (delete the first %)
+% \DescribeMacro{\macro}
+% Description and usage of the macro.
+%
+% The description will appear in the usage
+% part of the documentation. Use \subsubsection{} etc. for structuring.
+%
+% The implementation of the macros defined here has to be written in
+% chairxmathLinalg.dtx
+%\fi
+%
+%\subsubsection{General Linear Algebra}
+%
+%\DescribeMacro{\tr}
+% Trace of a linear map |\tr(A)|: $\tr(A)$ \\
+% Uses |operatorfont|.
+%
+%\DescribeMacro{\rank}
+% Rank of a linear map |\rank(A)|: $\rank(A)$ \\
+% Uses |operatorfont|.
+%
+%\DescribeMacro{\codim}
+% Codimension |\codim U|: $\codim U$ \\
+% Uses |operatorfont|.
+%
+%\DescribeMacro{\diag}
+% Diagonal (for filling matrices etc.)  |\diag(1,-1, -1)|: $\diag(1,-1, -1)$ \\
+% Uses |operatorfont|.
+%
+%\DescribeMacro{\Trans}
+% Transposition of matrices |A^\Trans|: $A^\Trans$ \\
+% Uses |scriptfont|.
+%
+%\DescribeMacro{\Mat}
+% Matrices |\Mat_n(\mathbb{R})|: $\Mat_n(\mathbb{R})$ \\
+% Uses |operatorfont|.
+%
+%\DescribeMacro{\SymMat}
+% Symmetric matrices |\SymMat_n(\mathbb{R})|: $\SymMat_n(\mathbb{R})$ \\
+% Uses |operatorfont|.
+%
+%\DescribeMacro{\ann}
+% Annihilator of a subspace |U^\ann|: $U^\ann$ \\
+% Uses |scriptfont|.
+%
+%\DescribeMacro{\Span}
+% Span of something |\Span\{v, u\}|: $\Span\{v, u\}$
+% and with optional argument
+% |\Span[\mathbb{C}]\{v,u\}|: $\Span[\mathbb{C}]\{v,u\}$ \\
+% Uses |operatorfont|.
+%
+%\DescribeMacro{\basis}
+% Font for basis vectors |\basis{e}_i|: $\basis{e}_i$ \\
+% Uses |basisfont|.
+%
+%\subsubsection{Tensors}
+%
+%\DescribeMacro{\tensor}
+% Generic tensor product over some ring |a \tensor b|: $a \tensor b$.\\
+% With optional subscript |V \tensor[\algebra{A}] U|: $V \tensor[\algebra{A}] U$
+%
+%\DescribeMacro{\Tensor}
+% Tensor powers, tensor algebra |\Tensor^\bullet(V)|: $\Tensor^\bullet(V)$ \\
+% Uses |operatorfont|.
+%
+%\DescribeMacro{\Anti}
+% Antisymmetric tensor powers, Grassmann algebra |\Anti(V)|: $\Anti(V)$
+%
+%\DescribeMacro{\Sym}
+% Symmetric tensor powers, symmetric algebra |\Sym^\bullet(V)|: $\Sym^\bullet(V)$ \\
+% Uses |operatorfont|.
+%
+%\DescribeMacro{\Symmetrizer}
+% Symmetrizer |\Symmetrizer_n|: $\Symmetrizer_n$
+%
+%\DescribeMacro{\AntiSymmetrizer}
+% Anti-symmetrizer |\AntiSymmetrizer|: $\AntiSymmetrizer$
+%
+%\DescribeMacro{\ins}
+% Generic insertion map |\ins_X|: $\ins_X$ \\
+% Uses |operatorfont|.
+%
+%\DescribeMacro{\jns}
+% Generic right insertion map |\jns_X|: $\jns_X$ \\
+% Uses |operatorfont|.
+%
+%\DescribeMacro{\insa}
+% Antisymmetric insertion map |\insa(X)|: $\insa(X)$ \\
+% Uses |operatorfont|, |scriptfont|.
+%
+%\DescribeMacro{\inss}
+% Symmetric insertion map |\inss(v)|: $\inss(v)$ \\
+% Uses |operatorfont|, |scriptfont|.
+%
+%\DescribeMacro{\dega}
+% Antisymmetric degree |\dega(a) = ka|: $\dega(a) = ka$ \\
+% Uses |operatorfont|, |scriptfont|.
+%
+%\DescribeMacro{\degs}
+% Symmetric degree |\degs(X) = \ell X|: $\degs(X) = \ell X$ \\
+% Uses |operatorfont|, |scriptfont|.
+%
+%\subsubsection{Inner Products}
+%
+%\DescribeMacro{\SP}
+% Simple scalar product |\SP{x, y}|: $\SP{x, y}$.
+%
+%\DescribeMacro{\littlepara}
+% Small parallel to be used as a subscript |v_\littlepara|: $v_\littlepara$
+%
+%\DescribeMacro{\IP}
+% Generic inner product with five arguments to decorate it |\IP[]{}{}{}{}{}| and an optional argument to adjust the size:
+%\[
+%\IP[\big]{}{B}{z, w}{\perp}{R}
+%\quad
+%\textrm{and}
+%\quad
+%\IP[\Big]{\perp}{\algebra{B}}{\prod x_i, y}{\prime}{\algebra{A}}
+%\]