Linear algebra (線形代数学): Concepts (概念)

Real numbers

• 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)

Expression (mathematics)

• 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)