I can't tell if this video is a good one or not. Linear Algebra just became so freaking hard and none of the math makes any sense. All these vector spaces and sub spaces are so abstract ughhhhh
I can assure you, the video is a good one 🤩🤩 He could've taken a little more time and explained each algebraic step he did. But he just stuck to the kernel part of it alone, in this specific video
How are you such an amazing teacher, seriously. It would also be really helpful if you numbered your videos so that we know what order to watch it in. but seriously these are amazing. thank you!!!!!
SO THAT IS THE NULL SPACE!!!!! :-O Why couldn't they explain this at the same time they explained us about the null space?!?!?! Now that I VISUALLY see it, I can really understand what we're talking about! Thanks Sal!!
At 0:13 when he coins the term "multiplation" :) Muchas gracias Khan Academy brothas! Your videos are helping me through grad school! Who needs professors on tenure anyways :)
I just wonder, that if you will combain the equations at time 7:45 it wil be a contradiction. Why, because: x1 = -3t and, ( x1 - 1 = 3t, gives x1 = 3t + 1), so ( x1 = -3t AND x1 = 3t = 1), but that is when solving 2 linear equations with 2 unknown, sorry, I'am bad. But it sure is a great video, very well. Rainer
I can't tell if this video is a good one or not. Linear Algebra just became so freaking hard and none of the math makes any sense. All these vector spaces and sub spaces are so abstract ughhhhh
7 years later, I'm feeling the same way! although the video was explained much better than my lecturer.
I feel you haha
I can assure you, the video is a good one 🤩🤩
He could've taken a little more time and explained each algebraic step he did. But he just stuck to the kernel part of it alone, in this specific video
How are you such an amazing teacher, seriously. It would also be really helpful if you numbered your videos so that we know what order to watch it in. but seriously these are amazing. thank you!!!!!
SO THAT IS THE NULL SPACE!!!!! :-O
Why couldn't they explain this at the same time they explained us about the null space?!?!?!
Now that I VISUALLY see it, I can really understand what we're talking about!
Thanks Sal!!
At 0:13 when he coins the term "multiplation" :)
Muchas gracias Khan Academy brothas! Your videos are helping me through grad school! Who needs professors on tenure anyways :)
Great explanation of the nullspace of T.
kernel== nullspace
Little hair splitting: Kernel is a kind of transformation. It’s not all the vectors. That is basically the difference with NULL.
Thanks for the explanations!
13:16 bookmark, a set of vectors in one domain gets mapped to just a single set in range. Yet still a linear trasforation..... neat
Thank you Sal
Gracias!
thank you
great explanation
good explanation
thx
does this have anything to do with the kernel trick in support vector machines? (machine learning)
does he mean the space spanned by the vectors S? because S itself is not a subspace.
i thought it would be shifted one up, how is it to the right?
I like to skip ahead and watch these advanced videos so that I can see what I will be able to understand someday.
I just wonder, that if you will combain the equations at time 7:45 it wil be a contradiction.
Why, because: x1 = -3t and, ( x1 - 1 = 3t, gives x1 = 3t + 1), so ( x1 = -3t AND x1 = 3t = 1), but that is when solving 2 linear equations with 2 unknown, sorry, I'am bad. But it sure is a great video, very well. Rainer
I am doing this freshman year help
lol multiplation :D