nonnegative eigenvector is often normalized so that the sum of its components is equal to unity; in this case, #eigenvector is vector of a #probability distribution and is sometimes called a stochastic eigenvector.

nonnegative eigenvector is often normalized so that the sum of its components is equal to unity; in this case, #eigenvector is vector of a #probability distribution and is sometimes called a stochastic eigenvector.

If A is row-stochastic then column vector with each entry 1 is an #eigenvector corresponding to #eigenvalue 1, which is also ρ(A) by remark above. It might not be only eigenvalue on unit circle: associated eigenspace can be multi-dimensional. If A is row-stochastic,irreducible

If A is row-stochastic then column vector with each entry 1 is an #eigenvector corresponding to #eigenvalue 1, which is also ρ(A) by remark above. It might not be only eigenvalue on unit circle: associated eigenspace can be multi-dimensional. If A is row-stochastic,irreducible

A very simple explanation of a recent maths paper (co-written by a University of California LosAngeles maths professor) on #eigenvector & #eigenvalue

— in the student newspaper of the same university by Shruti Iyer

@ashwin_baindur

https://dailybruin.com/2019/11/25/ucla-mathematician-helps-prove-simplified-equation-discovered-by-physicists/

不明覺厲

#線性代數 #eigenvalue #特徵值 #eigenvector #特徵向量

https://mp.weixin.qq.com/s/cJLQFljjbT0NzaiMR801aA

#Chladni #plate #acoustic #figure #animation each frame has lines at the nodes (non-moving points) of an #eigenvector of #biharmonic #operator , successive frames have decreasing #eigenvalue .

https://media.mathr.co.uk/mathr/2019-toot-media/mathr%20-%202019-06-24%20-%20biharmonic%20eigenvectors%20chladni%20plate%20-%20256x256p4.mp4

Implemented in #GNU #Octave using its #sparse #matrix eigensystem solver. I used a 5x5 kernel for the operator, based on the 3x3 Laplacian kernel convolved with itself, not 100% sure that this is the correct way to go about it but results look reasonable-ish.