Week 10 - Algebraic and Geometric Multiplicities of an Eigenvalue

[akmalanwar]

Key Points...
- Geometric multiplicity - The nullity of the matrix (eigenvectors)
- Algebraic multiplicity - The number of times you see the eigenvalue repeat in the matrix
- G.M = A.M in order for it to be diagonal
- G.M </= A.M

Note. In this Ex. the A.M was 1 bc eigenvalue at 2 only occurred once in the matrix. So was the Nullity[(3)Col's-(2)Leading 1's].

[postcanyonbike]

You explained it better in three minutes than my professor did in an entire lecture. Thanks!

[zhuaiden]

MOST BRIEF & HELPFUL VIDEO EVER SEEN! THANK YOU

[leaixenavier]

that’s cool but when do you explain what geometric multiplicity actually means?

At right around 2:05 in the video, you get the rank as 2 which makes sense but how do you then assume that the dimension of the null space is 1? Thanks!

[MrAstroKind]

Good stuff, thanks for the help-- straight to the point and clearly explained.

[tiburtiusmonica]

god bless
thanks a lot....
it was to the point without much exaggeration..

[emilywong]

2:50 I think I'm missing something, why is the dimension of the null space 1 if the result of A-2I is rank 2? Won't the nullity also be 2?

[raduandreicosmin]

2:07

Why does a rank = 2 mean that the dimension of the null space is = 1?

[vijeykrishnaa]

Thank you so much... Helped me a lot before exams!!

[magicatt]

Differential equations and maybe proof techniques?

[OX_]

This video might not get a lot of likes, but who puts them puts them with a reason, thanks

[kannanr]

That was a short and clear explanation..! 

[cindyshin]

Could someone please explain why dim(N(A-I)) =1???

[harveyluo]

what is wrong with your rank of A-2I matrix it should be 1 right???

[JAlternative]

Great explanation (: thank you Mathapptician.