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to code up an algorithm that implements the dot product lets take a look at two different versions of the dot product operation on the left hand side of the screen here we see the dot product as defined mathematically we start with two column vectors x and y both of which has m rows and one columns then we define the dot product operation between these column vectors to be the scalar valued output x dot y which is equal to x one times y one plus x two times y two plus all the way to the end xm times ym and we can write that as the sum going through the rows so ill use the index i we go from the first row then we multiply the entries in the first row x1 times y1 then we go to the second row the index updates plus x2 times y2 plus all the way to the end till we get to the nth row which is xm times ym lets visualize whats happening here in this definition when we start with column vectors x and y each of which have m rows we have these scalar valued entries which are called the indiv
