Detailed Question: In this assignment I want to show the proof of the question asked.
To complete the assignment, you can make use of book named - An Introduction to Support Vector Machines and other kernel-based learning methods by NELLO CRISTIANINI AND JOHN SHAWE-TAYLOR
Question: Kernel and dot product: Let B be a n x n positive semi-definite matrix. Show that K (x, z) = x'Bz defines a kernel ak(x, z) = <Φ(x)Φi(z)> = ∑i=1 n Φi(x) Φi(z) , where Φ defines the feature space. You can consider the book An Introduction to Support Vector Machines and other kernel-based learning methods by NELLO CRISTIANINI AND JOHN SHAWE-TAYLOR.