Linear Algebra 16h3: Algebraic Multiplicity Matches Geometric Multiplicty

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Комментарии
Автор

Is there a geometric explanation for why the geometric multiplicity can't be larger than the algebraic multiplicity? I can't intuitively see why there couldn't be a plane of vectors that is stretched by the same eigenvalue without that eigenvalue appearing twice in the characteristic polynomial.

moritzheppler
Автор

thanks a lot. you really make things easy :D

SelviaResearch
Автор

Oh man, you made my day. Thanks for the video!

sergiofonsecarodriguez
Автор

Dr Pavel, In your video example you deduce by inspection the eigenvectors for lamda = 3, but if you follow the algebraic procedure to get aigevectors, you can get for lammda = 3 only 1 eigenvector, the other eigenvector should be deduce by inspection. That makes me confused
If you see the way is solved the problem in the next video, the geometric multiplicity is given by the algebraic procedure
So, following the algebraic procedure I could say that the matrix in your example is defective, and you have shown by inspection it is not. I think, if there is geometric multiplicity is should be deduce in the algeraic process. Is not that way ?
Thanks in advance

gguevaramu