Orthonormal Basis

Orthonormal Basis #

A basis is orthonormal if its vectors are:

  • orthogonal to each other
  • each has unit length
\[ \langle \mathbf{e}_i, \mathbf{e}_j \rangle = \begin{cases} 1 & i=j \\ 0 & i\ne j \end{cases} \]

Why it matters: orthonormal bases make projections and computations simple.

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