 The dual form that arises in the creation of a kernel allows us to mathematically formulate a version of PCA in which we never actually solve the eigenvectors and eigenvalues of the covariance matrix in the formula_17-space (see Kernel trick).The N-elements in each column of "K" represent the dot product of one point of the transformed data with respect to all the transformed points (N points).Some well-known kernels are shown in the example below.