The orthogonal projection (or simply ``projection'') of
is defined by
The complex scalar
is called the
coefficient of projection
. When projecting
onto a unit
, the coefficient of projection is simply the inner
Motivation: The basic idea of orthogonal projection of onto
is to ``drop a perpendicular'' from onto to define a new
vector along which we call the ``projection'' of onto .
This is illustrated for in Fig.5.9 for and
, in which case
in 2D space.
Derivation: (1) Since any projection onto must lie along the
line collinear with , write the projection as
. (2) Since by definition the projection error
is orthogonal to , we must have
See §I.3.3 for illustration of orthogonal projection in matlab.
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