Commit 41e6ccd7 authored by Jim Hefferon's avatar Jim Hefferon

jc3

parent 7ebccd87
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......@@ -330,13 +330,13 @@ beginfig(8) % graph of rank falling and nullity rising
pickup pencircle scaled line_width_light;
drawpoint(z10);
pickup pensquare scaled line_width_light;
draw (x10,y10+0.5v)--(x10,y4-0.5v) withcolor .8white; % vert line above dot
draw (x10-.5whisker_width,y4-0.5v)--(x10+.5whisker_width,y4-0.5v) withcolor .8white; % whisker at top
draw (x10,y10+0.5v)--(x10,y4-0.5v) withcolor medgray; % vert line above dot
draw (x10-.5whisker_width,y4-0.5v)--(x10+.5whisker_width,y4-0.5v) withcolor medgray; % whisker at top
draw (x10-.5whisker_width,y10+0.5v)--(x10+.5whisker_width,y10+0.5v) withcolor .8white; % whisker at bot
label.rt(btex \small $\nullity (t^j)$ etex,(x10,.5[y10,y4]));
draw (x10,y10-0.5v)--(x10,1v) withcolor .8white; % vert line below dot
draw (x10-.5whisker_width,y10-0.5v)--(x10+.5whisker_width,y10-0.5v) withcolor .8white; % whisker at top
draw (x10-.5whisker_width,1v)--(x10+.5whisker_width,1v) withcolor .8white; % whisker at bot
draw (x10,y10-0.5v)--(x10,1v) withcolor medgray; % vert line below dot
draw (x10-.5whisker_width,y10-0.5v)--(x10+.5whisker_width,y10-0.5v) withcolor medgray; % whisker at top
draw (x10-.5whisker_width,1v)--(x10+.5whisker_width,1v) withcolor medgray; % whisker at bot
label.lft(btex \small $\rank (t^j)$ etex,(x10,.55[y10,1v]));
pickup pencircle scaled line_width_light;
drawpoint((1w,9v));
......@@ -351,13 +351,13 @@ beginfig(8) % graph of rank falling and nullity rising
% Generalized spaces
z20=(20w,2v); % were to anchor the line for generalized spaces
pickup pensquare scaled line_width_light;
draw (x20,y20+0.5v)--(x20,y4-0.5v) withcolor .8white; % vert line above dot
draw (x20-.5whisker_width,y4-0.5v)--(x20+.5whisker_width,y4-0.5v) withcolor .8white; % whisker at top
draw (x20-.5whisker_width,y20+0.5v)--(x20+.5whisker_width,y20+0.5v) withcolor .8white; % whisker at bot
draw (x20,y20+0.5v)--(x20,y4-0.5v) withcolor medgray; % vert line above dot
draw (x20-.5whisker_width,y4-0.5v)--(x20+.5whisker_width,y4-0.5v) withcolor medgray; % whisker at top
draw (x20-.5whisker_width,y20+0.5v)--(x20+.5whisker_width,y20+0.5v) withcolor medgray; % whisker at bot
label.rt(btex \small $\dim(\gennullspace{t})$ etex,(x20,.5[y20,y4]));
draw (x20,y20-0.5v)--(x20,1v) withcolor .8white; % vert line below dot
draw (x20-.5whisker_width,y20-0.5v)--(x20+.5whisker_width,y20-0.5v) withcolor .8white; % whisker at top
draw (x20-.5whisker_width,1v)--(x20+.5whisker_width,1v) withcolor .8white; % whisker at bot
draw (x20,y20-0.5v)--(x20,1v) withcolor medgray; % vert line below dot
draw (x20-.5whisker_width,y20-0.5v)--(x20+.5whisker_width,y20-0.5v) withcolor medgray; % whisker at top
draw (x20-.5whisker_width,1v)--(x20+.5whisker_width,1v) withcolor medgray; % whisker at bot
label.rt(btex \small $\dim(\genrangespace{t})$ etex,(x20,.8[y20,1v]));
endfig;
......
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......@@ -4,8 +4,8 @@
\section{Jordan Form}
\index{Jordan form|(}
\noindent\textit{This section uses material from three optional
subsections:~Direct Sum, Determinants Exist, and
Laplace's Expansion Formula.}
subsections:~Combining Subspaces, Determinants Exist, and
Laplace's Expansion.}
The chapter on linear maps shows that every $\map{h}{V}{W}$ can
be represented by a partial identity matrix with respect to some
......
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