الجبر متعدد الخطوط
In mathematics, multilinear algebra extends the methods of linear algebra. Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concepts of p-vectors and multivectors with Grassmann algebra.
الأصل
استخدم في الطوبولوجيا الجبرية
استنتاج بشأن النهج التجريدي
مواضيع في الجبر متعدد الخطوط
- tensor
- dual space
- bilinear operator
- inner product
- multilinear map
- Exterior algebra
- Cramer's rule
- component-free treatment of tensors
- Kronecker delta
- tensor contraction
- mixed tensor
- Levi-Civita symbol
- tensor algebra, free algebra
- symmetric algebra, symmetric power
- exterior derivative
- Einstein notation
- symmetric tensor
- metric tensor
There is also a glossary of tensor theory.
بعض الطرق التي يتم فيها تطبيق مفاهيم الجبر متعدد الخطوط
- classical treatment of tensors
- dyadic tensor
- bra-ket notation
- geometric algebra
- Clifford algebra
- pseudoscalar
- pseudovector
- spinor
- outer product
- hypercomplex number
- multilinear subspace learning
المصادر
- Hermann Grassmann (2000) Extension Theory, American Mathematical Society. Translation by Lloyd Kannenberg of the 1862 Ausdehnungslehre.
- Wendell H. Fleming (1965) Functions of Several Variables, Addison-Wesley.
- Second edition (1977) Springer ISBN 3540902066.
- Chapter: Exterior algebra and differential calculus #ستة in 1st ed, #سبعة in 2nd.
- Ricci-Curbastro, Gregorio; Levi-Civita, Tullio (1900), "Méthodes de calcul différentiel absolu et leurs applications", Mathematische Annalen 54 (1): 125–201, doi:, ISSN 1432-1807
