Last Updated
：2025/12/04
Grassmann algebra
Noun
(algebra)
A
direct
sum
with
an
exterior
product
of
multivector
spaces
which
are
all
based
on
a
same
underlying
finite-dimensional
vector
space.
The
associative
algebra
of
sums
and
exterior
products
of
scalars,
vectors,
blades,
multivectors,
and
hybrid
(i.e.,
non-homogeneous)
sums
of
multivectors
of
different
grades.
Japanese Meaning
Grassmann代数は、すべて同一の有限次元ベクトル空間に基づき、多重ベクトル空間の直和と外積という演算を持つ代数です。これは、スカラー、ベクトル、ブレード、多重ベクトル、および異なるグレード（次数）の多重ベクトルの非均質な和からなる結合代数である。
Sense（1）
(algebra)
A
direct
sum
with
an
exterior
product
of
multivector
spaces
which
are
all
based
on
a
same
underlying
finite-dimensional
vector
space.
The
associative
algebra
of
sums
and
exterior
products
of
scalars,
vectors,
blades,
multivectors,
and
hybrid
(i.e.,
non-homogeneous)
sums
of
multivectors
of
different
grades.
（ plural ）
Quizzes for review
(algebra) A direct sum with an exterior product of multivector spaces which are all based on a same underlying finite-dimensional vector space. The associative algebra of sums and exterior products of scalars, vectors, blades, multivectors, and hybrid (i.e., non-homogeneous) sums of multivectors of different grades.
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See correct answer
Grassmann algebra
In geometric algebra, the Grassmann algebra provides a unified associative framework of scalars, vectors, blades, and multivectors built from the exterior product over a finite-dimensional vector space.
See correct answer
In geometric algebra, the Grassmann algebra provides a unified associative framework of scalars, vectors, blades, and multivectors built from the exterior product over a finite-dimensional vector space.
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