Inner Product Calculator
Calculate the standard Euclidean inner product (often called the dot product in ℝⁿ) of two vectors. Enter the vector components separated by commas.
About the Inner Product
An inner product is a generalization of the dot product. For real vectors in Euclidean space (ℝⁿ), the standard inner product is identical to the dot product. It takes two vectors and returns a scalar value.
The formula for the standard Euclidean inner product of two vectors u = (u₁, ..., uₙ) and v = (v₁, ..., vₙ) is:
Inner products are fundamental in linear algebra and functional analysis, used to define concepts like length (norm), angle, and orthogonality in vector spaces.