Last Updated
：2025/11/20
affine transformation
Noun
(geometry,
linear
algebra)
A
geometric
transformation
that
preserves
lines
and
parallelism,
but
in
general
not
lengths
or
angles;
(more
formally)
an
automorphism
of
an
affine
space:
a
mapping
of
an
affine
space
onto
itself
that
preserves
both
the
dimension
of
any
affine
subspace
and
the
ratio
of
the
lengths
of
any
pair
of
parallel
line
segments.
Japanese Meaning
直線や平行性を保つが、必ずしも長さや角度を保たない幾何学的変換。 / アフィン空間上の自己写像で、各アフィン部分空間の次元や、並行な線分間の長さ比を保持する写像。
Sense（1）
(geometry,
linear
algebra)
A
geometric
transformation
that
preserves
lines
and
parallelism,
but
in
general
not
lengths
or
angles;
(more
formally)
an
automorphism
of
an
affine
space:
a
mapping
of
an
affine
space
onto
itself
that
preserves
both
the
dimension
of
any
affine
subspace
and
the
ratio
of
the
lengths
of
any
pair
of
parallel
line
segments.
（ plural ）
Quizzes for review
(geometry, linear algebra) A geometric transformation that preserves lines and parallelism, but in general not lengths or angles; (more formally) an automorphism of an affine space: a mapping of an affine space onto itself that preserves both the dimension of any affine subspace and the ratio of the lengths of any pair of parallel line segments.
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See correct answer
affine transformation
Applying an affine transformation to the set of points maps every line to a line and preserves parallelism, although distances and angles may change.
See correct answer
Applying an affine transformation to the set of points maps every line to a line and preserves parallelism, although distances and angles may change.
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