Linear Algebra 15o: The Null Space of a Linear Transformation

[@MathTheBeautiful]

Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.

[@vinylflouring]

Pavel is among the greatest math educatora of our time. This is the best soup to nuts linear algebra video series available.

[@zhuli693]

pretty good, very well explained. I am using this great lecture series to help my daughter. :)

[@SparkyElectricDave]

Hi, thank you for great videos, they have helped me to recall my high school topics but I still have some problem with the topic of Matrix on trying to bridge the gap over to Neural Networks for solving very big number of equations on solar planetary and just wonder if there are any good books or on line videos to bridge the gap and give an elementary treatment of the neural networks to bridge the gap between Matrices. Thanks again for your wonderful outstanding videos. Just love them.

[@RR42636]

Really, really good video. thanks!

[@klarabratteby5044]

The null space of the reflection transformation is the trivial null space. What is the column space of the reflection transformation?

[@MathTheBeautiful]

The entire space

[@klarabratteby5044]

​@@MathTheBeautiful So could you say that without the column-space there would not be a reflection?

[@labalimbu5153]

thank you sir

[@mathematicsplusplus]

Thank you for these wonderful lectures! Maybe you should make it clear that a "linear" function f(x) = ax + b is NOT linear in the sense of these videos, as the word "linear" is used with different meanings (affine vs. truly linear.) Keep up the great work!