We propose a novel algorithm based on Principal Component Analysis (PCA). First, we present an interesting approximation of PCA using Gram-Schmidt orthonormalization. Next, we combine our approximation with the kernel functions from Support Vector Machines (SVMs) to provide a nonlinear generalization of PCA. After benchmarking our algorithm in the linear case, we explore its use in both the linear and nonlinear cases. We include applications to face data analysis, handwritten digit recognition, and fluid flow.