From 8f3a3f952b0e5bd692b9b41d1417c877b0e0425e Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sun, 3 Nov 2019 20:57:10 -0500 Subject: [PATCH] mjo-linear_algebra: add the \rank{} of a matrix (or EJA, or...). --- examples.tex | 3 ++- mjo-linear_algebra.tex | 11 +++++++++++ 2 files changed, 13 insertions(+), 1 deletion(-) diff --git a/examples.tex b/examples.tex index c00279b..dde74d0 100644 --- a/examples.tex +++ b/examples.tex @@ -182,7 +182,8 @@ $L$ is $\adjoint{L}$, or if it's a matrix, then its transpose is $\transpose{L}$. Its trace is $\trace{L}$. Another matrix-specific concept is the Moore-Penrose pseudoinverse of $L$, denoted by - $\pseudoinverse{L}$. + $\pseudoinverse{L}$. Finally, the rank of a matrix $L$ is + $\rank{L}$. The span of a set $X$ is $\spanof{X}$, and its codimension is $\codim{X}$. The projection of $X$ onto $V$ is $\proj{V}{X}$. The diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex index e2ae9fa..204ad05 100644 --- a/mjo-linear_algebra.tex +++ b/mjo-linear_algebra.tex @@ -51,6 +51,17 @@ % The trace of an operator. \newcommand*{\trace}[1]{ \operatorname{trace}\of{{#1}} } + +% The "rank" of its argument, which is context-dependent. It can mean +% any or all of, +% +% * the rank of a matrix, +% * the rank of a power-associative algebra (particularly an EJA), +% * the rank of an element in a Euclidean Jordan algebra. +% +\newcommand*{\rank}[1]{ \operatorname{rank}\of{{#1}} } + + % The ``span of'' operator. The name \span is already taken. \newcommand*{\spanof}[1]{ \operatorname{span}\of{{#1}} } -- 2.44.2