12-240/Classnotes for Tuesday October 23: Difference between revisions

Latest revision as of 06:37, 22 October 2014

#	Week of...	Notes and Links
Additions to this web site no longer count towards good deed points.
1	Sep 10	About This Class, Tuesday, Thursday
2	Sep 17	HW1, Tuesday, Thursday, HW1 Solutions
3	Sep 24	HW2, Tuesday, Class Photo, Thursday
4	Oct 1	HW3, Tuesday, Thursday
5	Oct 8	HW4, Tuesday, Thursday
6	Oct 15	Tuesday, Thursday
7	Oct 22	HW5, Tuesday, Term Test was on Thursday. HW5 Solutions
8	Oct 29	Why LinAlg?, HW6, Tuesday, Thursday, Nov 4 is the last day to drop this class
9	Nov 5	Tuesday, Thursday
10	Nov 12	Monday-Tuesday is UofT November break, HW7, Thursday
11	Nov 19	HW8, Tuesday,Thursday
12	Nov 26	HW9, Tuesday , Thursday
13	Dec 3	Tuesday UofT Fall Semester ends Wednesday
F	Dec 10	The Final Exam (time, place, style, office hours times)
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Definition: L(V,W) is the set of all linear transformation L: V->W

u $\in \,\!$ V, 0 of L(V,W) (u)=0 of W (this is a l.t.str)

If L1 and L2 $\in \,\!$ L(V,W), (L1 + L2) (u)= L1(u) +L2(u) (this is a l.t.str)

If c $\in \,\!$ F and L $\in \,\!$ L(V,W), (c*L) (u)= c*L(u) (this is a l.t.str)

Theorem: L(V,W) is a vector space

Proof: "Distributivity" c(x+y)=cx+cy

In our case need to show c(L1 + L2)= cL1 + cL2

Where c $\in \,\!$ F and L1 and L2 $\in \,\!$ L(V,W)

(LHS) (u)

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 {{12-240/Navigation}}
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 Definition: L(V,W) is the set of all linear transformation L: V->W
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 == Lecture notes scanned by [[User:KJMorenz|KJMorenz]] ==
 <gallery>
-Image:12-240-Oct30-2.jpg
+Image:12-240-Oct30.jpg|Oct 30 Page 1
-Image:12-240-Oct30.jpg
+Image:12-240-Oct30-2.jpg|Oct 30 Page 2
+Image:12-240-Oct2.jpg|Oct 2 Page 1
+Image:12-240-Oct2-2.jpg|Oct 2 Page 2
+Image:12-240-Oct2-3.jpg|Oct 2 Page 3
+Image:12-240-Oct2-4.jpg|Oct 2 Page 4
+Image:12-240-Basis.jpg|Basis of a Vector Space
+Image:12-240-TutOct4.jpg|Tutorial Oct 4
 </gallery>