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.
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.
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.
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 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.
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.
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.
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 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!
did you graduate bro?
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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!!!!!
+TTbambam13 Holy shit! you go to imperial college london?
+Mostafa Adel Yeap! well.. where I really go to at the end of the day is Khan Ac!
@@TTbambam13 what a coincidence, I also go to Imperial just had my lecture on nullspaces then went here. xd
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!
Thank you so much for this amazing video! I am grateful for your help with my mathematics!
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.
Same for me... And never gives us the anwsers to the questions either so it feels pointless to do them
@@InzaneFlippers This seems like something you should be able to complain about
4:50 AM
5/5/2023
I watch these videos BECAUSE he explains it slowly and thoroughly. If it's too slow, forward the damn video!
Yess sirr!!
God Bless You
Skip lecture and listening to this is even better than wasting your time waking up early in the morning just for the god damn Eng. Maths Lecture.
Distributive property of Matrix dot vector product should have been proved first for 'closed under addition' proof.
To all people out there who I know are scratching their heads, let me lift a burden off your shoulders; Nullspace and Kernel is the same thing!
yeah i assumed they were thank you so much now I don't have to watch the video
each has a different frequency and operates within band with , annd moves on common frequinces
These are awesome. Hoping for more soon :).
Hi
you saved my day!
Too good
exam in 4 hours
Bruh, how's life after college? Im a college student in 2021, so I'm quite curious
hopefully you did well
What do you mean by; "Closed under addition" or "Closed under multiplication"?
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.
That means by adding or multiplying you won't leave the vector space.
Sal, can you start to add speed to the videos so we can watch it quicker and save time? Thanks.
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.
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.
I don't understand... Av1 = 0 and Av2 =0 then A( V1 + V2) = AV1 + Av2 isnt that only true if you take v1 and v2 to be 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.
kernel is some what same as nullspace
Thank you Sal Keeeeeeeep coming
I see... So it is the vector set that maps the matrix to the zero vector. Very deep concepts are they not?
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.
awww fun!.. this brings back memories! good explaining also
I was so bored after my A levels that I subconsciously began to make an expression for the number of vectors in a subspace.
This video would be MUCH better if he actually found the null space.
ooops wrong video my bad. This one actually helped a lot
lolol thanks for the laugh!
I am not worthy of your awesomeness
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.
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.
@mbueno Especially when you're primarily not studying mathematics.
So what is kernel?
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"
@mbueno My too :/
Thanks a lot!! The videos are very helpfull
is it related to IMRAN KHAN??
example please!
don't understand why the two terms exist then
which two terms?
what
gg
um... just skip through it then? dafuq...
*homogeneous
1.25x speed, thank me later