SciTech-Mathmatics - Advanced Linear Algebra(高等线性代数): Vector、Vectors、Vector Space 和 Matrix 的奇妙联系

SciTech-Mathmatics - Advanced Linear Algebra(高等线性代数):

Vector、Vectors、Vector Space和 Matrix 的奇妙联系

\(\large \begin{array}{llr} \bf{Vector \ Ops.} \begin{cases} Inner \ Product & \Leftrightarrow & \bf{行}乘\bf{列} \\ Linear\ Combination & \Leftrightarrow & Linear\ Combination \\ Outer \ Product & \Leftrightarrow & \bf{列}乘\bf{行} \end{cases} { \Bigg \} } \bf{Matrix \ Mul.} \end{array}\)

Inner Product(Vector) ⇔ 行乘列(Matrix Multiplication)

Outer Product(Vector) ⇔ 列乘行(Matrix Multiplication)

Linear Combination(Vectors) ⇔ Linear Combination(Matrix Multiplication)