Showing posts with label 多重線形代数. Show all posts
Showing posts with label 多重線形代数. Show all posts

Saturday, November 7, 2015

Multilinear algebra: Concepts

Function
  • Bilinear map
Abstract object
  • Tensor (intrinsic definition)
Formula
  • Cramer's rule
Vector space
  • Dual space
Mathematical notation
  • Einstein notation
Binary operation
  • Exterior product
One-form (A linear real-valued function)
  • exterior derivative
A generalization of the dot product
  • Inner product
Discrete version of the delta function
  • Kronecker delta
A three-index object
  • Levi-Civita symbol (Permutation symbol)
A function
  • Metric tensor
  • Multilinear map
Geometric object
  • Mixed tensor
  • Symmetric tensor
  • Tensor
Associative algebra
  • Symmetric algebra, Symmetric power

  • tensor algebra, free algebra
Operation
  • Tensor contraction