12-240/Classnotes for Tuesday November 6

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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)

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