This method was introduced by Karl Pearson. It works on a condition that while the data in a higher dimensional space is mapped to data in a lower dimension space, the variance of the data in the lower dimensional space should be maximum.
It involves the following steps:
Construct the covariance matrix of the data.
Compute the eigenvectors of this matrix.
Eigenvectors corresponding to the largest eigenvalues are used to reconstruct a large fraction of variance of the original data.
Hence, we are left with a lesser number of eigenvectors, and there might have been some data loss in the process. But, the most important variances should be retained by the remaining eigenvectors.