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I'm new to Data Science. I'm trying to understand cosine similarity and it seems like the equation is about finding the distance between two vectors. From what I've Googled, a vector needs to have magnitude and direction. But in CS, it seems like it's a 1-dimensional array. Is vector in CS the same as vector in Physics? If so, what is the direction of a vector. And if a vector is like this [1, 0, 1, 0] what is the magnitude of this vector?

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As you ask specifically for the Cosine Similarity technique, it has magnitude and direction, and similar to a vector which is used in Physics, as Cosine Similarity deals with vectors in an inner product space.

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So, the magnitude of vectors is exactly the same as the formula in Physics (summating over the squares of the vector elements.)

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Yes, they are the same.

The array [1, 0, 1, 0] represents a vector in $4$ dimensional euclidean space ($\mathbb{R}^4$) with tails at [0, 0 , 0 ,0] and head at [1, 0, 1, 0]. So your vector is "pointing" in the direction of your given set of coordinates.

This might be easier to visualize in $2$ dimensions: for example, the array [1,0] corresponds to the unit vector along the $x$-axis centered at the origin.

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