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| Angela Ruggiero |
Sunday, November 8, 2015
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
- Symmetric algebra, Symmetric power
- tensor algebra, free algebra
Operation
- Tensor contraction
Friday, November 6, 2015
Thursday, November 5, 2015
Linear algebra (線形代数学): Concepts (概念)
Real numbers
Expression (mathematics)
- Scalar (スカラー)
- Eigenvalue (固有値)
Geometric object
- Euclidean vector (空間ベクトル)
- Eigenvector (固有ベクトル)
Collection of geometric objects
- Vector space (ベクトル空間)
- Linear subspace (線形部分空間)
- Dual space (双対ベクトル空間)
- Kernel (linear algebra) (零空間)
Function (mathematics), mapping
- Vector projection ()
- Linear map (線形写像)
- Projection (linear algebra) (射影作用素)
Intersection of all subspaces
- Linear span (線形包)
Additional structure (付加構造)
- Inner product space (計量ベクトル空間)
Algebraic operation
- Dot product, scalar product (ドット積)
- Outer product, tensor product (直積)
- Linear independence (線形独立)
- Linear combination (線形結合)
Relation
- Orthogonality (直交)
Matrix (行列)
- Transpose (転置行列)
Method (アルゴリズム)
- Gram-Schmidt process (グラム・シュミットの正規直交化法)
- Ordinary least squares ()
Equation
- Linear equation (一次方程式)
Set of vectors (ベクトル集合)
- Basis (linear algebra) (基底)
Set of all possible column matrix (集合)
- Column space ()
- Row and column spaces (行空間)
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