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EECS 16B Lectures - Shared screen with speaker view
Ranelle
02:01:07
What’s good, 16B?!
Vanshaj Singhania
02:01:19
kinda hope this chat pops off like tuesday's
Ranelle
02:01:43
I put it on my insta story. 😂
Francisco G
02:01:58
MORNIN' GENTS
mjayasur
02:02:11
Morning!
ryanm
02:02:21
oy
Francisco G
02:02:27
sry, & Ladies
Anay Wadhera
02:02:31
lmao
Vron Vance
02:03:16
“distinguished guests”v (includes nonbinary folks)
Francisco G
02:03:48
^* ty
Francisco G
02:04:22
f- it, *MORNING EVERYBODY
Vron Vance
02:04:47
:) morn!
Francisco G
02:05:53
:)
dylanbrater
02:06:37
M*m
Vanshaj Singhania
02:06:41
lol
dylanbrater
02:06:52
Jk
Subham Dikhit
02:08:15
what do you mean by "intermediaries"
Stephen
02:08:19
bro... midterm2 season bouta begin...
Francisco G
02:08:42
c'mon now.. don't bring the mood down Stephen, lol
Akshay Ravoor
02:08:46
Intermediaries to calculate eigenvalues/vectors since we need a square matrix
Subham Dikhit
02:09:03
thx
vincentwaits
02:09:40
What is r in this case??
Stephen
02:09:44
rank
Andrew Fearing
02:09:47
does A have to be a real matrix?
vincentwaits
02:09:57
Ty
Anay Wadhera
02:10:01
Think so
Francisco G
02:10:38
very
Bryan Ngo
02:10:51
when would we use A^T A and AA^T
Jason Bustani
02:11:07
to get a smaller square matrix
Akshay Ravoor
02:11:07
I think sometimes it’s easier to find eigenvalues for one than other
Akshay Ravoor
02:11:14
e.g. see homework 8 prob 1
Jason Bustani
02:11:32
you see which gives you a smaller matrix
Vanshaj Singhania
02:11:44
does "complete set" just mean there's one for each eigenvalue?
Oliver Puffer
02:11:57
So the remaining zero valued eigenvectors are a complete set of orthonormal evectors?
vincentwaits
02:14:55
What is the vector ui again?
Alexander Yang
02:15:27
it makes matrix U needed for SVD
Vanshaj Singhania
02:18:49
it would be an approximation of A though right?
Balaji
02:18:57
No
Balaji
02:19:00
SVD is exact
Vanshaj Singhania
02:19:00
oh wait we're not ignoring any of the components nvm
mjayasur
02:21:16
eigenvalue
Oliver Puffer
02:24:39
Why is this number 2?
Brandon Fajardo
02:24:50
Second proof
Ashwat Chidambaram
02:24:58
He’s talking about “details”
Francisco G
02:25:18
imagine he started with"Given"
mjayasur
02:26:41
Matrix of u vectors?
Aidan Higginbotham
02:27:09
what fills the rest of the sigma matrix?
mjayasur
02:27:14
0's
Aidan Higginbotham
02:27:17
ty
mjayasur
02:27:20
np
Gilbert
02:29:13
u get the exact SVD
Jake Whinnery
02:29:21
A?
Vanshaj Singhania
02:29:31
hopefully A
Add
02:29:42
You get the summation on the right and A on the left right
Stephen
02:30:28
oh so since the V vectors are orthonormal, they are 1
Vanshaj Singhania
02:30:32
ahh
Alexander Yang
02:30:39
VV^T = I
Stephen
02:30:45
Lit
mjayasur
02:30:46
Show that vvT is idenitity
mjayasur
02:31:21
ooo cuz the orthonormal
Aidan Higginbotham
02:32:32
what are the remaining evectors?
mjayasur
02:33:00
i think the first r eigenvectors had eigenvalues that were positive, the rest have zero Eigen values so we are looking at those eigenvectors for v2
Vainavi Viswanath
02:33:00
The eigenvectors for eigenvalues of zero
Sal
02:33:04
invertible!
Stephen
02:33:05
identity
dylanbrater
02:33:09
I
Ayush Sharma
02:33:29
Would V not equal v_1 through v_n, not through v_r?
Mohsin Sarwari
02:33:45
it should, i think he made a typo
Ayush Sharma
02:33:52
OK!
Francisco G
02:33:53
hot mic
Stephen
02:34:05
is [V1 V2] = [v1 ... vr] or should it be = [v1...v.]?
Stephen
02:34:13
vn*
Calvin Yan
02:34:29
Yeah should be vn
Vanshaj Singhania
02:36:11
why can't we just show that V1V1T is I? as opposed to showing that VVT is I and then showing that AV2V2T is 0?
Mohsin Sarwari
02:36:38
+1
Akshay Ravoor
02:36:47
I think he’s trying to account for why we can just ignore the eigenvectors with zero eigenvalue when doing SVD
Jake Whinnery
02:37:12
0
mjayasur
02:37:20
The eigenvalues * the Eigen vectors
Sal
02:37:23
big lambda times A^T*V_2
Sal
02:37:30
L flipped those
Bryan Ngo
02:37:58
AV_2 = [λ_1 v_{r+1} λ_2 v_{r+2} ... ] = all zero matrix
Vanshaj Singhania
02:38:55
that makes sense @Akshay
Jake Whinnery
02:38:55
How did we prove AV1V1T = 1 again?
Vanshaj Singhania
02:39:12
we didn't, though I think you can say that because they're orthonormal
Vanshaj Singhania
02:39:24
V1V1T would be 1 one the diagonal and 0 everywhere else
Ashwat Chidambaram
02:39:47
^ yeah, ig there’s two ways to show it, we’re doing it the full way
Jake Whinnery
02:40:11
Ohh thank you
Ashwin Rammohan
02:40:14
magnitude^2
Bryan Ngo
02:40:17
||M||^2
Ashwin Rammohan
02:40:17
so M must be 0
James Shi
02:40:44
oh so since the diagonal of M^T M is 0, then M must be 0
Ashwat Chidambaram
02:41:10
No I believe M^T M should be a single 1x1 matrix, or single value
Ashwat Chidambaram
02:41:27
Actually nvm ignore that
Jake Whinnery
02:41:46
Did he just define M as AV2
Anay Wadhera
02:42:00
Looks like it
Sal
02:42:10
This is a side example
Sal
02:42:16
I think?
Ashwin Rammohan
02:42:25
why is that resulting matrix a diagonal matrix?
Ashwat Chidambaram
02:42:28
I think its just to prove the point that AV_2 is 0
mjayasur
02:42:30
he’s just proving a property
Ashwin Rammohan
02:42:31
MTM
Francisco G
02:44:03
I don't have a mic on my Desktop, sry Prof's
Sal
02:48:05
m<n?
Jake Whinnery
02:48:17
Smaller matrix size after
Aidan Higginbotham
02:48:44
whatever's smaller
Ayush Sharma
02:51:06
I remember we were talking yesterday about how SVDs are used for useful data extraction. Wouldn't a longer SVD (associated with using the bigger of A^T * A and A* A^T) be better in these cases, where there are more/different SVDs to choose from?
Ayush Sharma
02:51:14
Or, not yesterday, Tuesday.
Ayush Sharma
02:51:48
Oh, also, not more/different SVDs, it should be more/different sigma values.
Kunaal Sundara
02:51:56
it would have the same amount of singular values
Kunaal Sundara
02:52:05
since rank A = rank ATA = rank AAT
Ayush Sharma
02:52:10
Ohh yeah.
Alexander Yang
02:52:12
sometimes we are limited by data size, and one case may be more optimal than another
Ayush Sharma
02:52:13
OK, makes sense!
Ayush Sharma
02:52:32
OK, thanks @Kunaal and @Alexander! :)
Seth SANDERS
02:52:39
You are awesome!
Ranelle
02:52:55
Thank you. You are too, Professor Sanders!
Ayush Sharma
02:53:11
:D
Ashwat Chidambaram
02:53:13
so wholesome
Jake Whinnery
02:53:44
What’s the reason for switching notation from u to v?
Sal
02:54:20
u and v are different things and come from different places if it came from ATA or AAT
Stephen
02:54:20
columns vs rows
Calvin Yan
02:54:32
To keep things consistent. The u in the procedure for ATA are equivalent to the u in AAT
Jake Whinnery
02:54:35
Ohh ty
Francisco G
02:56:30
2
Kunaal Sundara
02:56:31
rank 2
Jake Whinnery
02:56:31
2
mjayasur
02:56:51
2
Bryan Ngo
02:56:52
2
Alexander Yang
02:56:58
any 2ers?
Ranelle
02:56:58
2 for no. 2 public uni
Francisco G
02:57:04
lmao
Jake Whinnery
02:57:06
oooooof
Michael Sparre
02:57:17
f
Francisco G
02:57:25
f
Stephen
02:57:28
wait, can someone say again what would you do if the rank is 1?
felixyu
02:57:30
f
Alexander Yang
02:57:53
if it is rank 1, we can find u and v by inspection to make A = ouv^T
Cooper
02:58:19
[25 7]
Cooper
02:58:21
[7 25]
Ayush Sharma
02:58:25
I think the very first example we did on Tuesday's class helps me a lot when thinking about a rank 1 matrix!
Vanshaj Singhania
02:58:25
that was wholesome
Alexander Yang
02:58:55
AA^T is diagonal lmao
Andrew Fearing
02:58:59
left is gooder
Sal
02:59:10
double plus extra gooder
Andrew Fearing
02:59:15
better*. lol this isn't words class
Sal
02:59:26
i wasn't making fun of you :(
Stephen
02:59:27
so rank 1 it's just the outer product?
Alexander Yang
02:59:34
yes @ Stephen
Bryan Ngo
03:00:15
u_1 = iu_2 = j
Andrew Fearing
03:01:32
yeah no worries i'm out of practice with communicating since the quarantine
hetalshah
03:01:43
Can someone explain why the eigenvectors are unit vectors for diagonal matrices?
Francisco G
03:01:51
i see v1 yus
Brandon Fajardo
03:02:22
Can't see
Alexander Yang
03:02:25
because the sigmas contain the magnitudes instead of having uv^T having magnitudes @hetalshah
Alexander Yang
03:02:50
we normalize u and v to generalize the process for all vectors
CharlieWu
03:03:11
wut does it mean for our rank to be 1?
Ayush Sharma
03:03:28
We only have one linearly independent column/row, and all others are linear combinations of that.
Ayush Sharma
03:03:42
I guess in a rank-1 case, it'd be a scaled version of that column/row.
Alexander Yang
03:04:21
rank 1 = the column space of the matrix has basis with just one vector
CharlieWu
03:04:31
oh ty
Ashwin Rammohan
03:05:12
Can't you swap the u's and v's?
Ashwin Rammohan
03:06:09
nvm
Vainavi Viswanath
03:07:10
if we had followed through with the example using ATA instead of AAT, would we still get the sam eigenvalues and u vectors and v vectors?
Jake Whinnery
03:07:24
I think yes
Vade Shah
03:07:25
Yes
mengzhusun
03:08:21
Are eigenvalues unique?
Francisco G
03:08:37
1,0 0,1
Francisco G
03:08:39
yep
Francisco G
03:11:44
PI/4:= myFav
Francisco G
03:11:51
theta
dylanbrater
03:14:30
Does this only apply when AA^T is Identity or is it simply when Eigen values are equal and if so do all the Eigenvalues need to be equal or just two?
Jake Whinnery
03:14:52
Why did AT become [-1 0; -1 0] instead of [1, 0; -1, 0]
dylanbrater
03:14:56
This new form of non-uniqueness I mean
Kunaal Sundara
03:15:08
I think that's part of the matrix bracket
Jake Whinnery
03:15:39
Lol thanks @kunaal
Jason Bustani
03:15:45
are we going to use SVD for sixt33n? what's the application for svd?
Akshay Ravoor
03:16:07
Voice analysis I’m guessing
Jake Whinnery
03:16:34
I think that’s the robot
Jake Whinnery
03:16:35
car
Aidan Higginbotham
03:16:36
That's the lab car
Qiyao Lai
03:16:47
yes
Andrew Fearing
03:17:13
lol what car #virtuallab
Alexander Yang
03:17:23
say 'corona' and 'quarantine', new left and right
Jason Bustani
03:17:42
thanks
Francisco G
03:17:54
ya, thanks professors.. keep up the good work
felixyu
03:17:57
:”)
Francisco G
03:18:12
enjoy your families... Classmates too. Stay Safe.Go Play Doom
felixyu
03:18:13
Will there be OH during break?
ryan m
03:18:26
What car
Cooper
03:18:30
🇨🇦
Stephen
03:19:10
!!!
Vanshaj Singhania
03:19:18
is module 3 content in scope for MT 2?
Stephen
03:19:20
Thank you professor
Jason Bustani
03:19:21
👌
Stephen
03:19:26
Wash them hands people
Add
03:19:30
Thanks
Subham Dikhit
03:19:32
PASS No Pass and Count As Major Req!!!
dylanbrater
03:19:32
Thank you
Alexander Yang
03:19:36
take long walks … in ur house
Aidan Higginbotham
03:19:36
Thank you Prof Gru and Prof Sanders!
Eric Chang
03:19:41
Thanks!
Jake Whinnery
03:19:42
Thanks professors! Have a great break and stay safe!
Cooper
03:19:47
Thanks!
Mohsin Sarwari
03:19:49
Thanks!
Brandon Fajardo
03:19:51
Thank you!
Joshua Baum
03:19:53
Thank You!
Jennifer Zhou
03:19:57
Thank you professor!!!
Ashwin Rammohan
03:20:09
Thank you Professors!
Sasha
03:20:17
Thank you, lectures have been great!!
Alexander Yang
03:20:19
thanks!
Stephen
03:20:19
thx profs
Gilbert
03:20:25
thank you professors!
Howard Ho
03:20:26
Thank you Professors!
Vainavi Viswanath
03:20:27
Thank you professors!
Calvin Yan
03:20:31
Thanks!
Jiachen Yuan
03:20:35
thx
Michael Sparre
03:20:43
Thanks professors!
Bryan Ngo
03:20:50
danke
Jason Bustani
03:21:03
🙏🧼🧼
Jason Bustani
03:21:45
wash🧼them hands🙏 folks 🙎‍♀️🙎‍♂️
Vanshaj Singhania
03:21:46
thank you professors! have a good break and stay safe :)
Ayush Sharma
03:21:52
Thanks a bunch, and stay stafe, y'all! :)
Jasmine Bae
03:22:01
Thank you!
Akshay Ravoor
03:22:03
Thank you both!
Catherine Hwu
03:22:04
Thank you!
Samuel Accurso
03:22:05
Thank you!!
Nicholas Berberi
03:22:06
thank you
Kunaal Sundara
03:22:06
thanks!
Kev
03:22:06
thanks
Qiyao Lai
03:22:08
ty
Ashwat Chidambaram
03:22:12
ty