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Spencer Kent's Personal Meeting Room - Shared screen with speaker view
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!