[Math] Eigenvectors and Principal component

abstract-algebraeigenfunctionseigenvalues-eigenvectorslinear algebra

What is the difference between eigenvectors and principal component. I got confused about this point because some researches reported that the principal components are the same eigenvectors of covariance matrix whereas, the others say that the principal components are the yield of eigenvectors (weights) of covariance matrix multiplied with the original data.

Please if some one can help me in this point.

Best Answer

Loosely speaking the eigenvectors are just the linear combinations of the original variables. Their eigenvalues which are associated with each principal component tell you how much variation in the data set is explained.

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