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