Three-dimensional linear transformations

What to learn

- How to do Three dimensional Matrix multiplication ## Description
- We already know multipling 2d matrix.
- Three-dimensional linear transformation applies the same principle.
- basis vector
    - i hat
    - j hat
    - k hat

    $$\begin{bmatrix}a & b & c\\ d & e & f\\ g & h & i\end{bmatrix}\begin{bmatrix}
    j & k & l\\ 
    m & n & o\\ 
    p & q & r
    \end{bmatrix}$$

    - [j m p]^T is that transformed i hat laned vector. and we want to know [j m p]^T will go.

    $$j\begin{bmatrix}
    a \\  d\\ g
    \end{bmatrix} + m\begin{bmatrix}
    b \\  e\\ h
    \end{bmatrix} + p\begin{bmatrix}
    c \\  f\\ i
    \end{bmatrix}$$

    - we can do iteratively to j hat and k hat, and get matrix multiplication result.

    $$\begin{bmatrix}aj+bm+cp & ak+bn+cq & al+bo+cr\\ dj+em+fp & dk+en+fq & dl+eo+fr\\ gj+hm+ip & gk+hn+iq & gl+ho+ir\end{bmatrix}$$

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