CORRECTION: Where the determinant is written with straight bars at 1:23, the non-diagonal entries should be negative, because it is det(lambda*I - A). Because of how we computed the characteristic polynomial, everything else is still correct. (namely, two negatives that should be there would have cancelled out if they were there, so our answer is unchanged) Consider supporting the production of this course by joining the channel! You get access to early and exclusive videos, music, and the lecture notes from the course at the premium level or above! ruclips.net/channel/UCyEKvaxi8mt9FMc62MHcliwjoin Linear Algebra course: ruclips.net/p/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG Linear Algebra exercises: ruclips.net/p/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc
Hi sir, I’m little confused on the example at 3:19, for the lambda = 3 case, why would we have the eigenvector ? I’ve tried it is correct but how do you find this? Is that because you need to fix the missing span for the another eigenvector for lambda=3?
Check out my video on eigenspaces and their bases to see the process: ruclips.net/video/1zKuZqJLmqQ/видео.html It comes down to Gaussian elimination and the number of free variables after completing that process. Each free variable admits an additional dimension to the corresponding eigenspace.
CORRECTION: Where the determinant is written with straight bars at 1:23, the non-diagonal entries should be negative, because it is det(lambda*I - A). Because of how we computed the characteristic polynomial, everything else is still correct. (namely, two negatives that should be there would have cancelled out if they were there, so our answer is unchanged)
Consider supporting the production of this course by joining the channel! You get access to early and exclusive videos, music, and the lecture notes from the course at the premium level or above!
ruclips.net/channel/UCyEKvaxi8mt9FMc62MHcliwjoin
Linear Algebra course: ruclips.net/p/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG
Linear Algebra exercises: ruclips.net/p/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc
Clear and easy to understand with great examples!
Hi sir, I’m little confused on the example at 3:19, for the lambda = 3 case, why would we have the eigenvector ? I’ve tried it is correct but how do you find this? Is that because you need to fix the missing span for the another eigenvector for lambda=3?
Check out my video on eigenspaces and their bases to see the process: ruclips.net/video/1zKuZqJLmqQ/видео.html
It comes down to Gaussian elimination and the number of free variables after completing that process. Each free variable admits an additional dimension to the corresponding eigenspace.
Thanks for helping me out
Hi , shouldn't the off-diagonal values of det(λI - A) be negative ?
Btw, thanks alot for your efforts
Yes, don't know how I missed that. Adding correction to pinned comment. Thanks!
This video really helped me out 😊
Glad to hear it - thanks for watching!
Algebraic? More like "All these videos are lit!" 🔥
Thank you!
@@WrathofMath Hey no problem! Just keep the videos comin'
thanks so much
Can lambda 0 possibly be a complex number?
Certainly! I discuss that situation some here: ruclips.net/video/-p0f4MQCx0s/видео.html
@@WrathofMath If I want to get the eigenbasis of a Linear Transformation Matrix, does the eigenvalue multiplicity matter?
Not 5 but 4