Additions to this web site no longer count towards good deed points.
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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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![12-240-ClassPhoto.jpg](/images/thumb/f/fc/12-240-ClassPhoto.jpg/310px-12-240-ClassPhoto.jpg) Add your name / see who's in!
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In this lecture, the professor concentrate on basics and related theorems.
Definition of basic
β
V is a basic if
1/ It generates ( span) V, span β = V
2/ It is linearly independent
theorems
1/ β is a basic of V iff every element of V can be written as a linear combination of elements of β in a unique way.
proof: ( in the case β is finite)
β = {u1, u2, ..., un}
(<=) need to show that β = span(V) and β is linearly independent.
The fact that β span is the fact that every element of V can be written as a linear combination of elements of β, which is given
Assume
ai.ui = 0 ai
F, ui
β
ai.ui = 0 =
0.ui
since 0 can be written as a linear combination of elements of β in a unique way, ai=0
i
Hence β is linearly independent
(=>) every element of V can be written as a linear combination of elements of β in a unique way.
So, suppose
ai.ui = v =
bi.ui
Thus
ai.ui -
bi.ui = 0
(ai-bi).ui = 0
Lecture notes scanned by Oguzhancan