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Principal Component Analysis (PCA) is the focusing on only the ‘principal components’ among the many dimensions of a data set, such that one is reducing the dimensions of that data set by ignoring the ‘non-principal’ parts.

PCA though, with eigen values & vectors, take on a slightly deeper approach. Typically, data sets that are handled under PCA are in a matrix format and the principal components, that are sought from a matrix would be a single vector column (or row) that is most significant among the other matrix vectors and would suffice as a representative of the entire matrix. As alluded in the intro above, this vector alone would hold the main components of the entire matrix, hence the name PCA. Identifying this vector though does not necessarily have to be done by eigen vectors & values, as Singular Value Decomposition (SVD) and the Power Iteration are other alternatives.

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