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Let <math>V</math> be a finite dimensional vector space over a field <math>F</math>. Let <math>B = {v_1, v_2, v_3, ..., v_n}</math> be an ordered basis of <math>V</math> and <math>v \in V</math>. Then <math>v = \displaystyle\sum_{i=1}^{n} c_iv_i</math> where <math>c_i \in F</math>. Then the '''coordinate representation''' of <math>v</math> is defined by <math>[v]_B = </math>. |
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Let <math>V</math> be a finite dimensional vector space over a field <math>F</math>, <math>B = {v_1, v_2, v_3, ..., v_n}</math> be an ordered basis of <math>V</math> and <math>v \in V</math>. Then <math>v = \displaystyle\sum_{i=1}^{n} c_iv_i</math> where <math>c_i \in F</math>. Then the '''coordinate representation''' of <math>v</math> is the column vector \begin{pmatrix}c_1\\c_2\\c_3\\.\\c_n\end{pmatrix}</math>. |
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Let <math>W</math> be a finite dimensional vector space over the same field <math>F</math>, <math>B = {v_1, v_2, v_3, ..., v_m}</math> be an ordered basis of <math>W</math>. Define a linear transformation <math>T:V \to W</math>. Then the matrix representation of <math>T</math> in the ordered bases <math>B, K</math> is the matrix |
Revision as of 18:42, 29 November 2014
Welcome to Math 240!
(additions to this web site no longer count towards good deed points)
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| #
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Week of...
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Notes and Links
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| 1
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Sep 8
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About This Class, What is this class about? (PDF, HTML), Monday, Wednesday
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| 2
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Sep 15
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HW1, Monday, Wednesday, TheComplexField.pdf,HW1_solutions.pdf
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| 3
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Sep 22
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HW2, Class Photo, Monday, Wednesday, HW2_solutions.pdf
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| 4
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Sep 29
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HW3, Wednesday, Tutorial, HW3_solutions.pdf
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| 5
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Oct 6
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HW4, Monday, Wednesday, Tutorial, HW4_solutions.pdf
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| 6
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Oct 13
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No Monday class (Thanksgiving), Wednesday, Tutorial
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| 7
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Oct 20
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HW5, Term Test at tutorials on Tuesday, Wednesday
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| 8
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Oct 27
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HW6, Monday, Why LinAlg?, Wednesday, Tutorial
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| 9
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Nov 3
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Monday is the last day to drop this class, HW7, Monday, Wednesday, Tutorial
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| 10
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Nov 10
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HW8, Monday, Tutorial
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| 11
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Nov 17
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Monday-Tuesday is UofT November break
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| 12
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Nov 24
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HW9
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| 13
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Dec 1
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Wednesday is a "makeup Monday"! End-of-Course Schedule, Tutorial
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| F
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Dec 8
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The Final Exam
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| Register of Good Deeds
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Add your name / see who's in!
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Boris
Coordinate and Matrix Representation Problems
Recall:
Let 
be a finite dimensional vector space over a field 
, 
be an ordered basis of and 
. Then 
where 
. Then the coordinate representation of 
is the column vector \begin{pmatrix}c_1\\c_2\\c_3\\.\\c_n\end{pmatrix}</math>.
Let 
be a finite dimensional vector space over the same field , 
be an ordered basis of . Define a linear transformation 
. Then the matrix representation of 
in the ordered bases 
is the matrix
