Transpose of Matrix


Matrix composed with 3 axis unit vectors x, y, z’s inverse matrix is an Identity matrix
$$\begin{pmatrix}\vec{x} & \vec{y} & \vec{z}\end{pmatrix}\begin{pmatrix}\vec{x} \\ \vec{y}  \\ \vec{z}\end{pmatrix}= I$$
### 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?



$$(AB)^T = B^TA^T$$
$$(a^TBc)^T = c^TB^Ta$$
$$a^T b = b^Ta$$


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
> [Transpose](https://en.wikipedia.org/wiki/Transpose)

> [Untitled](http://www.gatsby.ucl.ac.uk/teaching/courses/sntn/sntn-2017/resources/Matrix_derivatives_cribsheet.pdf)





