Inner Product Space

An inner product space¹ is a real or complex vector space that has an operation called an “inner product” defined for it. The inner product of two vectors is a scalar, and is typically denoted by angle brackets like $\langle a, b\rangle$.

This is a generalization of the dot product that is defined in Euclidean vector spaces ($a \cdot b = \sum a_i b_i $). The existence of an inner product also allows generalized definition of other concepts such as angles, lengths and orthogonality (zero inner product) between the vectors in the vector space.

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