Inner Product

An inner product is a mathematical operation that takes two vectors and returns a single number measuring how similar or aligned they are. In Euclidean space, it’s the sum of the products of corresponding components (e.g., (a \cdot b = a_1b_1 + a_2b_2 + \dots + a_nb_n)). It generalizes the dot product and defines geometric concepts like **length** and **angle** in vector spaces.