For computational efficiency in PCA, evaluation of covariance matrix is done as $C = AA^T$ instead of original $C=A^TA$. How can that be justified? What steps are needed then to recover the original information? Although I can find the beauty and idea of PCA algorithm, still having hard time understanding some concepts.
Note: Here $C$ is the covariance matrix and $A$ is the set of data vectors represented in a matrix.