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Additional
orthonormal basis
English Wikipedia - The Free Encyclopedia
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Orthonormal basis
In
mathematics
, particularly
linear algebra
, an
orthonormal basis
for an
inner product space
V
with finite
dimension
is a
basis
for
V
whose vectors are
orthonormal
, that is, they are all
unit vectors
and orthogonal to each other. For example, the
standard basis
for a
Euclidean space
R
n
is an orthonormal basis, where the relevant inner product is the
dot product
of vectors. The
image
of the standard basis under a
rotation
or
reflection
(or any
orthogonal transformation
) is also orthonormal, and every orthonormal basis for
R
n
arises in this fashion.
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