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