Pattern Recognition and Machine Learning
Knowledgeof multivariate calculusand basic linear algebra ... The exercises that appear at the end of every chapter form an important com-ponent of the book. Each exercise has been carefully chosen to reinforce concepts ... also like to thank Asela Gunawardana for plotting the spectrogram in Figure 13.1, and Bernhard Scho¨lkopf for permission ...
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www.microsoft.comSolutions 1.1–1.4 7 Chapter 1 Introduction 1.1 Substituting (1.1) into (1.2) and then differentiating with respect to wi we obtain XN n=1 XM j=0 wjx j n −tn xi n = 0. (1) Re-arranging terms then gives the required result.