Difference between revisions of "12240/Classnotes for Thursday November 8"
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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
