I just donated $10 to the Khan Academy. I wish I could donate my full tuition to you, as you deserve it more than my university, but I gave you what I could afford. Thank you so much, Sal!
Wow Sal ten thousand times better explained than any of my professors at Imperial, really man If I could I would donate my whole tuition to Khan Ac Awesome TED talk by the way!!!!!
My professor is actually good, but i was behind in class when this lesson was taught. Learning it for the exam now and this saved meeee. Thank you so much again Khan Academy!
My linear algebra professor never does examples. All theory, every lecture, every time. Exams are usually a huge question mark going in, as we don't know what to expect. And he doesn't "like" our textbook, so he doesn't look to pull questions from there. He makes his own. Sucks.
He means that you are "stuck" inside a space and cannot get out of it either by adding or multiplying the vectors that are members of that space. For example, if you have two column vectors with 3 elements, and the third element is 0 in both of them, then you can never add them or multiply them in any way that changes the third element into something else than 0 - so those vectors will always have a 0 as the third elements. One example of a subspace is a 2D-plane in a 3D-space. Of course, since you are able to multiply the vectors with any number, a subspace must also include the zero vector.
If I'm following what you're saying correctly, doesn't he already say that when he mentions: "V1, V2 [- (that's the 'element'/pitchfork symbol) N", where N is every "x" vector that will make the statement "[A]x = 0-vector" true?
I think not necessarily... If the numbers are right, then when you multiply a matrix * vector (A*v1) the result can be zero vector *_even though_* the vectors themselves are *_not_* zero vector. Example: Matrix: [1, -3, -2] [-5, 9, 1] Vector: [5] [3] [-2] Multiply together and we get zero vector.
I think your videos are good, and they do explain. I think they would be much better if you did a couple run-throughs or had written down what you wanted to say. For example, you say you will set up the homogeneous equation, then you say you will talk about why it's HMGN, then you say, well I'll tell you in a second. That's unnecessary repetition that makes the videos seem longer than they are. I end up forwarding through about half of all your videos. Keep you the great work.
I read on mathstackexchange.com: "Physical meaning of null space" the null space is like the set of vectors that _get_ mapped to the zero vector _by_ the matrix! Like with linear transformations they say. These concepts provoke deep thought indeed.
umm no. Clicking 10 times on each vid to skip 3 secs each time then going back cos i skipped to far etc.. is just a hassle. If i am taking notes as well then 2x speed is so much easier.
Except when you do that, you may miss things. Just because you like to watch a video with things explained slowly and thoroughly doesn't mean everybody else should, does it? I for one can focus a lot better when I play it at 1.5 or 2 times the speed.
It has the same meaning as Null space _in this case_. But Kernel is a more "general" term in maths that applies to other concepts besides subspaces. But if somebody asks "Find the kernel of a matrix" they are basically saying "find the null space of a matrix"
I have to agree with Something so Original, he repeats himself a lot. Sure I forward, then I have to go back to see what I missed. It would be helpful if he was not so all over the place with his thoughts.
