Matrix in 3 dimension

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3-D

Extend 2-D to 3-D, each direction has 3 elements.

Combine these transformed vector by column, we can get transformation matrix.

Rotate 90 degree on y-axis

We can also apply this transformation matrix to a vector that needs to be transformed.

3-D matrix multiplication is like doing a transformation after another in 2-D.

Reference
https://www.3blue1brown.com/topics/linear-algebra