12-240/Classnotes for Tuesday November 6: Difference between revisions
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{{12-240/Navigation}} |
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==Riddle== |
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Find A and B such that AB - BA = I |
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==Theorems== |
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1. Given U with basis <math>\alpha</math>, V with basis <math>\beta</math>, W with basis <math>\gamma,</math> |
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<math>[T \circ S]_\alpha^\beta = [T]_\beta^\gamma \times [S]_\alpha^\beta</math> |
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2. For A <math>\in M_(m \times n)</math> and B <math>\in M_(n \times p)</math> and C <math>\in M_(p \times q)</math>, |
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(AB)C = A(BC) |
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== Lecture notes scanned by [[User:Zetalda|Zetalda]] == |
== Lecture notes scanned by [[User:Zetalda|Zetalda]] == |
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<gallery> |
<gallery> |
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Latest revision as of 04:52, 7 December 2012
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Riddle
Find A and B such that AB - BA = I
Theorems
1. Given U with basis [math]\displaystyle{ \alpha }[/math], V with basis [math]\displaystyle{ \beta }[/math], W with basis [math]\displaystyle{ \gamma, }[/math] [math]\displaystyle{ [T \circ S]_\alpha^\beta = [T]_\beta^\gamma \times [S]_\alpha^\beta }[/math]
2. For A [math]\displaystyle{ \in M_(m \times n) }[/math] and B [math]\displaystyle{ \in M_(n \times p) }[/math] and C [math]\displaystyle{ \in M_(p \times q) }[/math], (AB)C = A(BC)
Lecture notes scanned by Zetalda
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