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Dot Product via Elementwise Multiplication and Summation
The dot product of two vectors can be conceptually and practically understood as a two-step process: first, performing an elementwise multiplication between the two vectors to yield a new vector of the same length, and second, calculating the sum of all elements within that resulting vector.
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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.Weighted Sum via Dot Product
Cosine of Angle via Dot Product
Cosine Similarity