The QWP always transforms circularly polarized light into linearly polarized light. The multiplicity gives the number of linearly independent eigenvectors corresponding to each eigenvalue. Thus, determinants can be used to characterize linearly dependent vectors. This corresponds to the maximal number of linearly independent columns of formula 1. Single layer perceptrons are only capable of learning linearly separable patterns. There will be linearly independent solutions to each eigenvalue equation. It can distinguish data that is not linearly separable. Bound proteins are eluted out by utilizing a gradient of linearly increasing salt concentration. For other propagation directions the light will split into two linearly polarized beams. Let formula 52 be linearly independent vectors in formula 8. We claim that the vectors formula 24 are linearly independent. Recall that every basis of consists of exactly linearly independent vectors. We need to define one formula 91 matrix with linearly independent columns. Let be a square matrix with linearly independent eigenvectors (where ). This integral is a real number which depends linearly and continuously on formula 1.