What does a Principal Component in a PCA signify? How can we represent them mathematically?

Data Science, AI and ML
#1

The Principal Component represents a line or an axis along which the data varies the most and it also is the line that is closest to all of the n observations in the dataset.

In mathematical terms, we can say that the first Principal Component is the eigenvector of the covariance matrix corresponding to the maximum eigenvalue.

Accordingly,

  • Sum of squared distances = Eigenvalue for PC-1
  • Sqrt of Eigenvalue = Singular value for PC-1