TR3.5

Basis Inclass

Huxley Marvit 2021-10-04 Mon 09:20

#flo #inclass


1 Basis

title: lemma
something you prove with the intention to prove something else

easy way to check if something if linearly dependent: if there are more vectors than dimension!

  • spanning sets need to be >= len as the dimension
    • else it wont have all the nessasarry info
    • but it needs to be the same as the dimension for it to be a basis
      • linearly independent and spanning

1.0.1 One way to get anywhere = one way to get 0

true for 0, true for any other vec - KBxChapter2BReading#criterion for basis - going over the proof for this.

1.0.2 making something a basis

  • linearly independent can be added to and turned into a basis,
  • spanning set can be removed from and turned into a basis