Difference between revisions of "12-240/Classnotes for Thursday November 8"
From Drorbn
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== Goals == | == Goals == | ||
− | 1. compute Rank T over A | + | 1. compute Rank T over A<br> |
− | 2. Compute <math>T^ | + | 2. Compute <math>T^{-1}</math> over <math>A^{-1}</math><br> |
3. Solve systems of linear equations | 3. Solve systems of linear equations | ||
Revision as of 17:51, 3 December 2012
Contents |
Riddle Along
Four cars drive in the Sahara desert at constant speeds and with constant directions. A meets B, C, D; B meets C, D. Do C and D meet?
Goals
1. compute Rank T over A
2. Compute over
3. Solve systems of linear equations
Theorems
1. Given V' -> V -> W -> W' (where the linear transformations are Q, T, P respectively)
such that P and Q are invertible (i.e. Q is surjective and P is injective)
then rank T = rank PTQ
2. if T: V -> W, V with basis and W with basis
rank = rank T
3. if P and Q are invertible matrices, A is some other matrix, rank A = rank PAQ
Definitions
if A = , then it is linear transformation
Lecture notes upload by yaaleni.vijay
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