Inner Products

Inner Products #

  • generalise the dot product
  • define angles and projections
  • measures similarity between vectors
\[ \langle \mathbf{u}, \mathbf{v} \rangle = \mathbf{u}^T\mathbf{v} \]

It determines angles and orthogonality, and it induces a norm:

\[ \lVert \mathbf{u} \rVert = \sqrt{\langle \mathbf{u}, \mathbf{u} \rangle} \]

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