240AlgebraI-121023, Hours 19-20: Linear Transformations
October-18-12
9:32 AM
Read Along: Sections 2.1-2.4
Term Test: Thu Oct 25 3-5PM, Examination Facility room EX 200 (east side of McCaul St., near College).
Riddle Along: 1 2 3 4 5 6 7 8 9
  Two players alternate drawing cards from the above deck. The first player to have 3 cards that add up to 15, wins. Would you like to be the first to move or the second? (More on today's web, including a video link).
Following 09-240 hour 16, taught by Yael Karshon:
"T:V->W is linear"
Preserving 0.
Claim on cx+y.
Example: R^2->R^2 by explicit formula.
Example: Differentiation, multiplication by x.
Example: Matrices and linear transformations on F^n.
Example: Rotation (+ explicit formula).
Claim on differences and many-element sums.
Added 2012: \calL(V,W) is a vector space.
Composition of linear trans is a linear trans.
Composition is non-commutative. Example: differentiation and muliplication by x.
For a l.t., arbitrary values on a basis.
"Isomorphism".