kipriyanovichAn **Eigenvector** of matrix A is a non-zero vector that only scales (doesn't change direction) when A acts on it (`Av=λv`). **Eigenvalue** (λ) is the scalar. Pro-Tip: Key for stability & system analysis!
Statistics GlobeIn PCA, eigenvalues represent the variance explained by each principal component, while eigenvectors determine the direction of these components, illustrating how the original variables are weighted.
More info in my online course: https://statisticsglobe.com/online-course-pca-theory-application-r
#DataScience #PCA #Eigenvalues #Eigenvectors #RProgramming #DataAnalysis
Bruce Elrick
@hesss.bsky.socialI plan my routes (hiking, running, cycling) using heatmaps of other people's trips in @Strava.
How can we prevent converging to an equilibrium where we just copy shitty routes from ready other? Does the answer involve #eigenvectors?
jprbarry#Eigenvectors and #eigenvalues are beaut things. They are ESNTL for doing Principal Component Analysis (#PCA) which is an imp. technique in #UnsupervisedLearning. #PCA allows us to greatly reduce the dimensionality of datasets and keep most of the imp. info
https://bit.ly/3vWv1dH
https://bit.ly/3vWv1dH
nopeMining of Massive Datasets
(2014) : Leskovec, Jure and Rajaraman, Anand and Ullman, Jeffrey David
DOI: https://doi.org/10.1017/CBO9781139924801
#PCA #SVD #advertising #algorithm #big_data #clustering #data_mining #eigenvalues #eigenvectors #large_sca
#my_bibtex
(2014) : Leskovec, Jure and Rajaraman, Anand and Ullman, Jeffrey David
DOI: https://doi.org/10.1017/CBO9781139924801
#PCA #SVD #advertising #algorithm #big_data #clustering #data_mining #eigenvalues #eigenvectors #large_sca
#my_bibtex
xameerhttps://math.stackexchange.com/a/6260?stw=2 - Answer:
Do matrices have to commute in order to share #eigenvectors and/or vice versa?
Do matrices have to commute in order to share #eigenvectors and/or vice versa?
unlike orbital angular momentum the #eigenvectors are not spherical harmonics.
unlike orbital angular momentum the #eigenvectors are not spherical harmonics.
normalized #eigenvectors of a circulant matrix are the #Fourier modes