Transpose of Matrix

Creator
Creator
Seonglae Cho
Created
Created
2022 Oct 28 17:26
Editor
Edited
Edited
2023 Apr 17 16:6
Refs
Refs
Matrix composed with 3 axis unit vectors x, y, z’s inverse matrix is an Identity matrix
(xyz)(xyz)=I\begin{pmatrix} \vec{x} & \vec{y} & \vec{z} \end{pmatrix} \begin{pmatrix} \vec{x} \\ \vec{y} \\ \vec{z} \end{pmatrix} = I

But

I felt weird and realized it is different from normal matrix multiplication
  • why vector is in matrix?
  • why use dot product instead of number multiplication? Is it valid?
 
 
 
(AB)T=BTAT(AB)^T = B^TA^T(aTBc)T=cTBTa(a^TBc)^T = c^TB^TaaTb=bTaa^T b = b^Ta
 
 
곱할때 Transpose 앞뒤적용할 지 선택할 때 일단 행렬크기 먼저 고려하고 더하고 옆에 빼는 다른 항의
그다음 크기가 작은 결과 행렬을 선택하여 계산하는 것이 좋다
보통 앞의 것 transpose
 
 
 
 

Diverse Attributes

 
 

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