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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.Dot Product via Elementwise Multiplication and Summation
Weighted Sum via Dot Product
Cosine of Angle via Dot Product