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CHAPTER 1: Linear Systems

CHAPTER 2: Vector Spaces

CHAPTER 3: Maps Between Spaces

CHAPTER 4: Determinants

CHAPTER 5: Similarity

Apendix

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Wikified by Carlos Rodriguez

If you find a typo please fix it! (the magic word is “thelab”).

This site is based on PmWiki. PmWiki is a wiki-based? system for collaborative creation and maintenance of websites. 

 PmWiki pages look and act like normal web pages, except they have an “Edit” link that makes it easy to
 modify existing pages and add new pages into the website, using basic editing? rules. 
 You do not need to know or use any HTML or CSS.  Page editing can be left open to the public or
 restricted to small groups of authors.

For more information look at DocumentationIndex.

This site does LATEX

wfy: Perl script to help wikify Linearalgebra


#!/usr/bin/perl

# section and base number
$S = 1;
$X = 1;

while (<>)
{
# $..$ ==> {$..$}
	s/\$([^\$]+)\$/{\$$1\$}/g;
# \begin{eq..} ==> \n=|[$ $$\n\begin{equation*}
	s/(\\begin\{eq.+\})/\n=|[\$ \$\$\n$1/;
# \end{eq..} ==> \n=|[$ $$\n\end{equation*}
	s/(\\end\{eq.+\})/$1\n\$\$ \$]\n/;
# \( ==> {$
	s/\\\(/{\$/g;
# \) ==> $}
	s/\\\)/\$}/g;
# \begin{definition} ===> "\n>>bgcolor=lightblue<<\n!!!! S.X Definition"
	if (/\\begin{def.+}/) {
	s/(\\begin{def.+})/\n>>bgcolor=lightblue<<\n!!!! $S.$X Definition/;
	$X = $X + 1;
	}
# \end{definition} ==> >><<
	s/\\end{definition}/>><<\n/;

# \begin{example} ===> !!!! X.X Example
	if (/\\begin{example}/) {
	    s/(\\begin{example})/\n!!!! $S.$X Example/;
	    ++$X;
	}
# \end{example} ==> \n
	s/\\end{example}/\n/;

# \begin{theorem} ==> "\n>>bgcolor=lightblue<<\n!!!! X.X Theorem"
	if (/\\begin{theorem}/) {
	    s/(\\begin{theorem})/\n>>bgcolor=lightblue<<\n!!!! $S.$X Theorem/;
	    ++$X;
	}
# \end{theorem} ==> >><<
	s/\\end{theorem}/>><<\n/;

# \begin{lemma} ==> !!!! x.x Lemma
	if (/\\begin{lemma}/) {
	    s/\\begin{lemma}/\n!!!! $S.$X Lemma/;
	    ++$X;
	}
# \end{lemma} ==> \n
	s/\\end{lemma}/\n/;

# \begin{remark} ==> !!!! x.x Remark
	if (/\\begin{remark}/) {
	    s/\\begin{remark}/\n!!!! $S.$X Remark/;
	    ++$X;
	}
# \end{remark} ==> \n
	s/\\end{remark}/\n/;

# \begin{proof} ==> !!!!! PROOF: 
	s/\\begin{proof}/\n!!!!! PROOF:\n/;

# \end{proof} ==> '''''QED'''''
	s/\\end{proof}/'''''QED'''''/;

# \vec{u} ==> \vec{ $u$ }
	s/\\vec{u}/\\vec{ \$u\$ }/g;
# \vec{a} ==> \vec{ $a$ }
	s/\\vec{a}/\\vec{ \$a\$ }/g;
# \Dash ==> --
	s/\\Dash/--/g;

# \label{abc} ==> [[#abc]]
        s/\\label{(.+?)}/[[#$1]]/;

# \nearbyxxx{abc} ==> [[#abc | nearbyxxx]]
	s/\\nearby(.+?){(.+?)}/[[#$2 | nearby$1]]/;

# \begin{align*} ==> \n=|[$ $$\n\begin{align*}
	s/(\\begin{ali.+})/\n=|[\$ \$\$\n$1/;
# \end{ali.} ==> \end{ali.}\n$ $$]\n
	s/(\\end{ali.+})/$1\n\$\$ \$]\n/;

# \begin{multl.} ==> \n=|[$ $$\n\begin{multl.}
	s/(\\begin{multl.+})/\n=|[\$ \$\$\n$1/;
# \end{multl.} ==> \end{multl.}\n$ $$]\n
	s/(\\end{multl.+})/$1\n\$\$ \$]\n/;

# \index{...} ==>
	s/\\index{.+}/ /;

# \noindent ==>
	s/\\noindent//;

# \begin{corollary} ==> !!!! x.x Corollary
	if (/\\begin{corollary}/) {
	    s/\\begin{corollary}/\n!!!! $S.$X Corollary/;
	    ++$X;
	}
# \end{corollary} ==> \n
	s/\\end{corollary}/\n/;

# \includegraphics{ch1.1} ==> =|Attach:ch1.1.png
	s/^.*\\includegraphics{(ch.+)}/=|Attach:$1.png/;

# \index{...} ==>  
    s/\\index{.+}//g;
# \definend{...}\index{..} ==> ''...''
    s/\\definend{(.+)}/''$1''/;
# ` ==> '
    s/`/'/g;
# ~ ==> 
    s/~/ /g;
# \Dash ==> --
    s/\\Dash/--/g;
# \/ ==>
    s/\\\///g;


	print;

}

wex: Perl Script to wikify Exercises


#!/usr/bin/perl

# Chapter, Section, Subsection, Number
$C = "Three";
$S = "VII";
$B = 4;
$N = 1;
$M = "Markov Chains";
$CSB = "$C.$S.$B";

$abc = "a";

while (<>)
{
# \begin{answer}...\end{answer} ==> delete
    if (/\\begin{answer}/) {
	while(!/\\end{answer}/) {
	    $_ = <>;
	}
	$_ = <>;
    }

# \begin{exercises} ==> !Exercises: C.S.B M
    s/\\begin{exercises}/(:title Exercises $CSB --- $M:)\nColor codes: %red%recommended%%, %blue%basic%%, %purple%puzzle%%\n/;
# \end{exercises} ==> 
    s/\\end{exercises}//;

# \recommended \item ==> red
    if (/\\recommended\s?\\item/) {
	s/^.*\\recommended\s?\\item/* %red%$CSB%%.$N /;
	++$N;
    }
# \puzzle \item ==> purple
    if (/\\puzzle\s?\\item/) {
	s/^.*\\puzzle\s?\\item/*.%purple%$CSB%%.$N /;
	++$N;
    }

# \item ==> blue
    if (/\\item/) {
	s/^.*\\item/* %blue%$CSB%%.$N /;
	++$N;
    }

# $..$ ==> {$..$}
	s/\$([^\$]+)\$/{\$$1\$}/g;
# \begin{exparts*} ==>  re-start $abc
    if (/\\begin{ex.+}/) {
	$abc = "a";
	s/(\\begin\{exp.+\})//;
    }
# \end{exparts*} ==>
    s/\\end{exp.+}/ /;

# \partsitem ==> **(a)
    if (/\\partsitem/) {
	s/^.*\\partsitem(.*)/**($abc)$1/;
	++$abc;
    }
# \begin{linsys} ==> \n=|[$ $$\n\begin{linsys}...
    s/[\$]?(\\begin{linsy.+)/\n=|[\$ \$\$\n$1/;
# \end{linsys} ==> \n$$ $]\n
    s/(\\end\{linsys\}).*/$1\n\$\$ \$]\n/;



# \end{exp..} ==> \n=|[$ $$\n\end{exp..}
	s/(\\end\{exp.+\})/$1\n\$\$ \$]\n/;
# \begin{eq..} ==> \n=|[$ $$\n\begin{equation*}
	s/(\\begin\{eq.+\})/\n=|[\$ \$\$\n$1/;
# \end{eq..} ==> \n=|[$ $$\n\end{equation*}
	s/(\\end\{eq.+\})/$1\n\$\$ \$]\n/;

# \( ==> {$
	s/\\\(/{\$/g;
# \) ==> $}
	s/\\\)/\$}/g;

# \vec{u} ==> \vec{ $u$ }
	s/\\vec{u}/\\vec{ \$u\$ }/g;
# \vec{a} ==> \vec{ $a$ }
	s/\\vec{a}/\\vec{ \$a\$ }/g;
# \Dash ==> --
	s/\\Dash/--/g;

# \begin{align*} ==> \n=|[$ $$\n\begin{align*}
	s/(\\begin{ali.+?})/\n=|[\$ \$\$\n$1/;
# \end{ali.} ==> \end{ali.}\n$ $$]\n
	s/(\\end{ali.+?})/$1\n\$\$ \$]\n/;

# \begin{multl.} ==> \n=|[$ $$\n\begin{multl.}
	s/(\\begin{multl.+?})/\n=|[\$ \$\$\n$1/;
# \end{multl.} ==> \end{multl.}\n$ $$]\n
	s/(\\end{multl.+})/$1\n\$\$ \$]\n/;

# \index{...} ==>
	s/\\index{.+?}/ /;
# \definend{...} ==> ''...''
	s/\\definend{(.+?)}/''$1''/;

# \noindent ==>
	s/\\noindent//;

# ` ==> '
    s/`/'/g;
# ~ ==> 
    s/~/ /g;
# \Dash ==> --
    s/\\Dash/--/g;
# \/ ==>
    s/\\\///g;

# \label{abc} ==> [[#abc]]
        s/\\label{(.+?)}/[[#$1]]/;

# \nearbyxxx{abc} ==> [[#abc | nearbyxxx]]
	s/\\nearby(.+?){(.+?)}/[[#$2 | nearby$1]]/;


# \includegraphics{ch1.1} ==> =|Attach:ch1.1.png
	s/^.*\\includegraphics{(ch.+?)}/=|Attach:$1.png/;


	print;

}

wnum: Perl Script to renumber exercises


#!/usr/bin/perl

$N = 1;

while(<>) {
    if (/[IV]+.[0-9]+%%\.[0-9]+/){
	s/([IV]+.[0-9]+%%\.)[0-9]+/$1$N/;
	++$N;
    }
    print;
}

‘macros.el’‘: Elisp macros


;; grb next link
(fset 'grab
   [?\C-s ?C ?H ?\C-b ?\C-b ?\C-  ?\C-e escape ?w])

;; put TOC trail at the end of the current buffer
(fset 'trail
   [escape ?> return return ?% ?t ?r ?a ?i ?l ?% ?< ?< ?| ?W ?i ?k ?i ?p ?u ?b ?l ?i ?s ?h ?e ?r ?/ ?T ?a ?b ?l ?e ?O ?f ?C ?o ?n ?t ?e ?n ?t ?s ?| ?> ?> ?\C-c ?\C-c ?\C-x ?k return])

;; wikify linearalgebra region
(fset 'wfy
   [?\C-u escape ?| ?~ ?/ ?w ?f ?y return])

;; wikify exercises region
(fset 'wex
   [?\C-u escape ?| ?~ ?/ ?w ?E ?x return])

;; need to change the CHAPTER3.OrthogonalProjectionIntoALine for what you want
(fset 'nearbyexample
   "\C-snearbyexample\C-b\C-r[[\C-f\C-fCHAPTER3.OrthogonalProjectionIntoALine\C-e")

;; need to change the CHAPTER3.OrthogonalProjectionIntoALine for what you want
(fset 'nearbylemma
   "\C-snearbylemma\C-b\C-r[[\C-f\C-fCHAPTER3.OrthogonalProjectionIntoALine\C-e")

;; need to change the CHAPTER3.OrthogonalProjectionIntoALine for what you want
(fset 'nearbytheorem
   "\C-snearbytheorem\C-b\C-r[[\C-f\C-fCHAPTER3.OrthogonalProjectionIntoALine\C-e")

;; need to change the CHAPTER3.OrthogonalProjectionIntoALine for what you want
(fset 'nearbyexercise
   "\C-snearbyexercise\C-b\C-r[[\C-f\C-fCHAPTER3.OrthogonalProjectionIntoALine\C-e")

;; need to change the CHAPTER3.OrthogonalProjectionIntoALine for what you want
(fset 'nearbycorollary
   "\C-snearbycorollary\C-b\C-r[[\C-f\C-fCHAPTER3.OrthogonalProjectionIntoALine\C-e")

;; need to change the CHAPTER3.OrthogonalProjectionIntoALine for what you want
(fset 'nearbydefinition
   "\C-snearbydefinition\C-b\C-r[[\C-f\C-fCHAPTER3.OrthogonalProjectionIntoALine\C-e")










;; run C-u 100 M-x dollar then this function that runs all the others
(fset 'r011
   [escape ?x ?e ?q ?* return escape ?x ?e ?q ?* ?e return escape ?x ?e ?q ?n ?* return escape ?x ?e ?q ?n ?* ?e return escape ?x ?r ?1 return escape ?x ?r ?2 return escape ?x ?r ?3 return escape ?x ?r ?4 return escape ?x ?r ?5 return escape ?x ?r ?6 return escape ?x ?r ?7 return escape ?x ?r ?8 return escape ?x ?r ?9 return escape ?x ?r ?1 ?0 return escape ?x ?r ?1 ?1 return])


;; $..$ ==> {$..$}  (but one at a time!!)
(fset 'dollar
   [?\C-s ?$ ?\C-b ?\C-  ?\C-s ?\C-s ?\C-s ?\C-b ?\C-f ?\C-w ?{ ?\C-y ?}])

;; $..$  ==> {$..$}
(fset 'rdollar
   [escape ?x ?q ?u ?e tab ?- ?r tab return ?\\ ?$ ?\\ ?( ?[ ?^ ?\\ ?$ ?] ?+ ?\\ ?) ?\\ ?$ return ?{ ?$ ?\\ ?1 ?$ ?} return ?! ?\C-x ?\C-x])


;; \begin{eqnarray*} ==> \n=|[$ $$ \begin{eqnarray*}
(fset 'eqn*
   [escape ?\C-% ?\\ ?\\ ?b ?e ?g ?i ?n ?{ ?e ?q ?n ?a ?r ?r ?a ?y ?\\ ?* ?} return ?\\ ?, ?\" ?\\ ?n ?= ?| ?[ ?$ ?  ?$ ?$ ?  ?\\ ?\\ ?b ?e ?g ?i ?n ?{ ?e ?q ?n ?a ?r ?r ?a ?y ?* ?} ?\" return ?! ?\C-x ?\C-x])


;; \end{eqnarray*} ==> \end{eqnarray*} $$ $]\n
(fset 'eqn*e
   [escape ?\C-% ?\\ ?\\ ?e ?n ?d ?{ ?e ?q ?n ?a ?r ?r ?a ?y ?\\ ?* ?} return ?\\ ?, ?\" ?\\ ?\\ ?e ?n ?d ?{ ?e ?q ?n ?a ?r ?r ?a ?y ?* ?} ?  ?$ ?$ ?  ?$ ?] ?\\ ?n ?\" return ?! ?\C-x ?\C-x])


;; \begin{equation*}  ==>  =|[$ $$ \begin{equation*}
(fset 'eq*
   [escape ?% ?\\ ?b ?e ?g ?i ?n ?{ ?e ?q ?u ?a ?t ?i ?o ?n ?* ?} return ?= ?| ?[ ?$ ?  ?$ ?$ ?  ?\\ ?b ?e ?g ?i ?n ?{ ?e ?q ?u ?a ?t ?i ?o ?n ?* ?} return ?! ?\C-x ?\C-x])

;; \end{equation*}  ==>  \end{equation*} $$ $]
(fset 'eq*e
   [escape ?% ?\\ ?e ?n ?d ?{ ?e ?q ?u ?a ?t ?i ?o ?n ?* ?} return ?\\ ?e ?n ?d ?{ ?e ?q ?u ?a ?t ?i ?o ?n ?* ?} ?  ?$ ?$ ?  ?$ ?] return ?! ?\C-x ?\C-x])


;; \( ... \)  ===>  {$ ... $}
(fset 'r1
   [escape ?% ?\\ ?( return ?{ ?$ return ?! ?\C-x ?\C-x escape ?% ?\\ ?) return ?$ ?} return ?! ?\C-x ?\C-x])

;; \begin{definition} ===> ">>bgcolor=lightblue<<\n!!!! X.X Definition"
(fset 'r2
   [escape ?\C-% ?\\ ?\\ ?b ?e ?g ?i ?n ?{ ?d ?e ?f ?i ?n ?i ?t ?i ?o ?n ?} return ?\\ ?, ?\" ?> ?> ?b ?g ?c ?o ?l ?o ?r ?= ?l ?i ?g ?h ?t ?b ?l ?u ?e ?< ?< ?\\ ?n ?! ?! ?! ?! ?  ?X ?. ?X ?  ?D ?e ?f ?i ?n ?i ?t ?i ?o ?n ?\" return ?y ?\C-x ?\C-x])


;; \end{definition} ===> >><<
(fset 'r3
   [escape ?% ?\\ ?e ?n ?d ?{ ?d ?e ?f ?i ?n ?i ?t ?i ?o ?n ?} return ?> ?> ?< ?< return ?! ?\C-x ?\C-x])


;; \begin{example} ===> !!!! 2.3 Example
(fset 'r4
   [escape ?% ?\\ ?b ?e ?g ?i ?n ?{ ?e ?x ?a ?m ?p ?l ?e ?} return ?! ?! ?! ?! ?  ?2 ?. ?5 ?  ?E ?x ?a ?m ?p ?l ?e return ?! ?\C-x ?\C-x])

;; \end{example} ===>
(fset 'r5
   [escape ?% ?\\ ?e ?n ?d ?{ ?e ?x ?a ?m ?p ?l ?e ?} return return ?! ?\C-x ?\C-x])

;; \begin{theorem} ==> ">>bgcolor=lightblue<<\n!!!! X.X Theorem"
(fset 'r6
   [escape ?\C-% ?\\ ?\\ ?b ?e ?g ?i ?n ?{ ?t ?h ?e ?o ?r ?e ?m ?} return ?\\ ?, ?\" ?> ?> ?b ?g ?c ?o ?l ?o ?r ?= ?l ?i ?g ?h ?t ?b ?l ?u ?e ?< ?< ?\\ ?n ?! ?! ?! ?! ?  ?X ?. ?X ?  ?T ?h ?e ?o ?r ?e ?m ?\" return ?! ?\C-x ?\C-x])

;;\end{theorem} ==>  >><<
(fset 'r7
   [escape ?% ?\\ ?e ?n ?d ?{ ?t ?h ?e ?o ?r ?e ?m ?} return ?> ?> ?< ?< return ?! ?\C-x ?\C-x])

;; \begin{lemma} ==> !!!! x.x Lemma
(fset 'r8
   [escape ?% ?\\ ?b ?e ?g ?i ?n ?{ ?l ?e ?m ?m ?a ?} return ?! ?! ?! ?! ?  ?X ?. ?X ?  ?L ?e ?m ?m ?a return ?! ?\C-x ?\C-x])

;; \end{lemma} ==> 
(fset 'r9
   [escape ?% ?\\ ?e ?n ?d ?{ ?l ?e ?m ?m ?a ?} return return ?! ?\C-x ?\C-x])

;; \begin{proof} ==> !!!!! PROOF: 
(fset 'r10
   [escape ?% ?\\ ?b ?e ?g ?i ?n ?{ ?p ?r ?o ?o ?f ?} return ?! ?! ?! ?! ?! ?  ?P ?R ?O ?O ?F ?: ?  return ?! ?\C-x ?\C-x])

;; \end{proof} ==> {$\diamond$} 
(fset 'r11
   [escape ?% ?\\ ?e ?n ?d ?{ ?p ?r ?o ?o ?f ?} return ?{ ?$ ?\\ ?d ?i ?a ?m ?o ?n ?d ?$ ?} return ?! ?\C-x ?\C-x])

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Page last modified on 01 June 2009, at 10:56 AM