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! th-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin Linear Algebra course: th-cam.com/play/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG.html Linear Algebra exercises: th-cam.com/play/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc.html
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: th-cam.com/video/1zKuZqJLmqQ/w-d-xo.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.
![DIRTY Shortcut to Find Geometric Multiplicity [Passing Linear Algebra]](http://i.ytimg.com/vi/FVRQqCV63TU/mqdefault.jpg)
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!
th-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin
Linear Algebra course: th-cam.com/play/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG.html
Linear Algebra exercises: th-cam.com/play/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc.html
Clear and easy to understand with great examples!
Algebraic? More like "All these videos are lit!" 🔥
Thank you!
@@WrathofMath Hey no problem! Just keep the videos comin'
Thanks for helping me out
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: th-cam.com/video/1zKuZqJLmqQ/w-d-xo.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.
This video really helped me out 😊
Glad to hear it - thanks for watching!
thanks so much
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!
Can lambda 0 possibly be a complex number?
Certainly! I discuss that situation some here: th-cam.com/video/-p0f4MQCx0s/w-d-xo.html
@@WrathofMath If I want to get the eigenbasis of a Linear Transformation Matrix, does the eigenvalue multiplicity matter?
Not 5 but 4