Rishi Shah

26:15

oh so sorry

Daniel Guzman

29:24

Oh sorry

Aditya Varma

31:29

0

Daniel Guzman

31:30

0?

Aayush Dave

31:30

0

Daniel Man

37:34

can you explain that last fact again

Daniel Man

37:39

about the product of eigenvalues

Anthony Jang

40:58

If det(A) = 0 then you know there is at least one eigenvalue that has a value of 0 (by def. det(A) = product of eigenvalues). And then he said “if you know the matrix A is not invertible, then there must be an eigenvalue of 0”. Dunno why though. @Daniel Man

Daniel Man

41:35

Ah okay thanks ^^

Anthony Jang

42:05

npnp

Daniel Guzman

43:49

@Anthony the last thing he said is becauses det[ A - (lambda)I] = 0 is how you find each eigenvalue. If lambda = 0, that implies det[A - 0] = 0, meaning det(A) = 0. So when det(A) = 0, that directly implies there is some eigenvalue of A must be 0.

Anthony Jang

45:40

Gotcha, ty.

Steven

45:45

n

Daniel Guzman

45:48

Tne order is n

Daniel Guzman

45:51

The*

Aayush Dave

51:35

1 0

Aayush Dave

51:37

And 0 1

Aayush Dave

54:05

Same polynomial

Aayush Dave

54:11

As last time

Aayush Dave

54:25

(3- lambda)(3-lambda)

Daniel Guzman

54:29

(3-lambda)^2

Steven

54:30

^

Emily Greer

56:42

0 1

Steven

56:43

Span{[1 0]}

Emily Greer

57:09

oh my bad

Emily Greer

57:21

yes

Aayush Dave

59:09

So does the one eigenvector correspond to both eigenvalues?

Emily Greer

01:00:34

yeah I believe so since both eigenvalues are 3

Aayush Dave

01:00:38

Shouldn’t there be a 0 0

Emily Greer

01:01:00

that is the trivial solution

Daniel Guzman

01:02:05

@ aayush [0 0] is in the span{[1 0]}

Aayush Dave

01:02:17

I see

Aayush Dave

01:02:22

Thank yall

Aditya Varma

01:02:45

Imaginary eigenvalues

Anthony Jang

01:03:15

Aren’t imaginary eigenvalues out of scope

Aditya Varma

01:06:57

1

Josh Kavilaveettil

01:06:58

1

Daniel Guzman

01:06:59

1

Steven

01:07:07

What is the general form of the rotation matrices?

Emily Greer

01:07:22

ad-bc = 0-(1)(-1) = 1

Daniel Guzman

01:07:36

any non-identity matrix where det(A) = 1

Steven

01:08:57

And the rotation direction is always counterclockwise, right?

Daniel Guzman

01:09:48

negative angles can rotate it clockwise I believe

Steven

01:12:03

@Daniel I think my question should be theta > 0 => counterclockwise and theta < 0 => clockwise?

Daniel Guzman

01:12:19

Yes, I think that's correct

Steven

01:12:27

Thanks!

Ayush Gupta

01:17:08

Thanks!