TR3.5

Taproot 2021-10-02 Sat 10:58

1 Why columns (not rows)?

1.1 Because columns map to input, while rows map to output

1.2 Linear dependence is going to have more to do with the columns

1.3 Dot products are "linear combinations" of the columns

1.4 It's only because we usually multiply with variables on the right. When we go backwards, then we care about the row.

2 #definiton column space   definition

The subpsace that gets hit by inputs.

3 Row vs Column linear dependency

3.1 Under what circumstances is it true that row linear independence iff column linear independence?

3.1.1 maybe in square matrices?