Dot product: Component vs. Geometric definition
Read OriginalThis article provides a clear mathematical proof showing why the component definition (sum of products of corresponding components) and the geometric definition (product of magnitudes times cosine of the angle) of the vector dot product are equivalent. It includes a geometric proof using the law of cosines and a projection proof using orthonormal basis vectors. The content is focused on linear algebra concepts relevant to computer science, graphics, and machine learning.
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