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Remember the calculated eigenvalues and eigenvectors of the matrix when learning linear algebra, and then this matrix can use this feature and feature value vector representation.
This can be understood as a vector matrix is actually more pieces together, so that you can establish contact matrices and vectors.
Eigenvalues and eigenvectors is actually seeking a combination of original vector representation of the easiest, because the vector can be decomposed and combinations.
Why eigenvalues and eigenvectors: The reason is decoupled, equivalent transformation.
What is it PCA: Principal Component Analysis, is to select the eigenvalues larger feature vector instead of the original eigenvalues and eigenvectors achieve dimensionality reduction,
Advantage of dimension reduction is to reduce the calculation amount, the disadvantage is the loss of accuracy.