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Weighted Sum via Dot Product
A fundamental application of the dot product is the computation of a weighted sum. Given a vector of values and a corresponding vector of weights , the weighted sum of the elements in based on the weights in can be concisely represented as the dot product .
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Pictorial Representation of Dot Product
Outer Product
In a simplified model for analyzing text, two words are represented by the numerical vectors A = [4, -2, 1] and B = [3, 5, 6]. To compute a similarity score, an operation is performed where the corresponding elements of the two vectors are multiplied together, and the resulting products are then summed to produce a single number. What is the final similarity score?
Calculating a Weighted Final Grade
Consider two numerical lists,
X = [1, 5, 3]andY = [2, 4]. The operation that multiplies corresponding elements and sums the results can be successfully performed on these two lists to produce a single numerical value.You are given two lists of numbers representing a shopping trip. The first list,
Quantities = [3, 1, 2], represents the number of each item bought. The second list,Prices = [2, 5, 4], represents the price of each corresponding item. To find the total cost of the shopping trip, you must perform a specific sequence of calculations. Arrange the following steps in the correct order to calculate the total cost.Dot Product via Elementwise Multiplication and Summation
Weighted Sum via Dot Product
Cosine of Angle via Dot Product