Let R H, where H is a Hilbert space, be the feature map. Let K R...

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Let R H, where H is a Hilbert space, be the feature map. Let K R" x R"R be the corresponding kernel function, i.., K(r, y) ((x), 6(y)) for all , y e R". We used the following linear equations in the proof of representer theorem: a- o), d()0, j- 1,..., N (3) where N are the unknowns, a is a given vector in H, and r TN are given vectors in R" Assume the kernel function K symmetric positive definite, i.e., for any natural number m and distinct vectors z, 2,.,zm R", the matrix K K(z, z) R xm is symmetric positive definite. Prove that the linear equation (3) has a unique solution Let R H, where H is a Hilbert space, be the feature map. Let K R" x R"R be the corresponding kernel function, i.., K(r, y) ((x), 6(y)) for all , y e R". We used the following linear equations in the proof of representer theorem: a- o), d()0, j- 1,..., N (3) where N are the unknowns, a is a given vector in H, and r TN are given vectors in R" Assume the kernel function K symmetric positive definite, i.e., for any natural number m and distinct vectors z, 2,.,zm R", the matrix K K(z, z) R xm is symmetric positive definite. Prove that the linear equation (3) has a unique solution