12-240/Classnotes for Thursday October 11: Difference between revisions
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ex: dim P(F)= <math>\infty \!\,</math> |
ex: dim P(F)= <math>\infty \!\,</math> |
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3/ Assume dim V = n < <math>\infty \!\,</math> then, |
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a) If G generate V then |G|<math>\ge \!\,</math> n & some set of G is a basic of V. ( If |G|= n, itself is a basic) |
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b) If L is linearly independent then |L|<math>\le \!\,</math> n, if |L|=n then L is a basic, if |L|< n then L can be extended to become a basic. |
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== Lecture notes scanned by [[User:Oguzhancan|Oguzhancan]] == |
== Lecture notes scanned by [[User:Oguzhancan|Oguzhancan]] == |
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Revision as of 16:43, 12 October 2012
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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.
Lecture notes scanned by Oguzhancan
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