WEB: faculty.washington.edu/kutz/a... This lecture focuses on algorithms for eigen-decompositions. Specifically, we consider the Rayleigh quotient and power iterations for producing eigenvalue and eigenvectors.
Пікірлер: 11
@shawqifarea6963 жыл бұрын
Thank you professor for this fantastic lecture! At around 4:10, the professor says: Hermitian matrices have m distinct eigenvalues. I think that is not always true, however. One counterexample is the mxm identity matrix: although it is Hermitian (i.e., symmetric), it has only one single eigenvalue (which is one) with an algebraic multiplicity of m.
@jimlbeaver3 жыл бұрын
Great stuff. I hadn't really gone through this before. Makes good sense...thanks for the clear explanation.
@robwindey92232 жыл бұрын
Great explanation!
@JuanGarcia-lo2el2 жыл бұрын
You are the best! I would like to attend some of your classes.
@vinaykumar-dp8ej2 жыл бұрын
Thanks a lot sir 🙏 very well explained 🙏
@mkelly663 жыл бұрын
I'm probably missing something, but shouldn't the equation for the eigenvalue lambda (visible at the bottom right at 26:00) also be divided by v-transpose times v?
@rajinish03 жыл бұрын
v is w/norm(w) which already normalized; so v^T times v is 1.
@5f3759df3 жыл бұрын
The Reighley quotient iteration can give you m eigenvalues and eigenvectors? In my intuition, I think this algorithm still procudes only the largest eigenvalue, but with cubic convergence speed compared to the standard power iteration. Am I right?
@Brien8313 жыл бұрын
The so called min max method uses the rayleigh quotient to give all eigenvalues.
@5f3759df3 жыл бұрын
@@Brien831 Just have Googled this min max theorem. Thanks a lot!