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Week of...
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Notes and Links
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1
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Sep 10
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About This Class, Tuesday, Thursday
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2
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Sep 17
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HW1, Tuesday, Thursday, HW1 Solutions
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3
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Sep 24
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HW2, Tuesday, Class Photo, Thursday
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4
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Oct 1
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HW3, Tuesday, Thursday
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5
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Oct 8
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HW4, Tuesday, Thursday
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6
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Oct 15
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Tuesday, Thursday
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7
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Oct 22
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HW5, Tuesday, Term Test was on Thursday. HW5 Solutions
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8
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Oct 29
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Why LinAlg?, HW6, Tuesday, Thursday, Nov 4 is the last day to drop this class
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9
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Nov 5
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Tuesday, Thursday
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10
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Nov 12
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Monday-Tuesday is UofT November break, HW7, Thursday
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11
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Nov 19
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HW8, Tuesday,Thursday
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12
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Nov 26
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HW9, Tuesday , Thursday
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13
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Dec 3
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Tuesday UofT Fall Semester ends Wednesday
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F
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Dec 10
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The Final Exam (time, place, style, office hours times)
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Register of Good Deeds
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Add your name / see who's in!
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In this lecture, the professor concentrate on corollaries of basic and dimension.
Annoucements
TA Office Hours (Still pending!) @ 215 Huron St., 10th floor.
Peter - 11am - 1pm
Brandon 1pm - 3pm
Topic: Replacement Theorem
corollaries
1/ If V has a finite basic β1, then any other basic β2 of V is also finite and |β1|=|β2|
2/ "dim V" makes sense
dim V = |β| if V has a finite basic β
Otherwise, dim V =
ex: dim P(F)=
3/ Assume dim V = n < then,
a) If G generate V then |G| n & some set of G is a basic of V. ( If |G|= n, itself is a basic)
b) If L is linearly independent then |L| n, if |L|=n then L is a basic, if |L|< n then L can be extended to become a basic.
Proofs
1) β2 generate and β1 is linearly independent
From replacement theorem
|β2| |β1| , ( role reversal), |β1| |β2|
Then |β2|= |β1|
3) a) (|G| n)
by dim V = n, exist basic β of V with n elements, Take L = β in the replacement lemma, |G| = n1
|L| n1= |G|
Hence n |G|
Lecture notes scanned by Oguzhancan