Transition Matrix for Axes Rotation in 3D and 2D | Linear Algebra

[@WrathofMath]

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[@raulbeienheimer]

BTW: I really like the way you illustrated the change of reference system that keeps a visual picture of the invariance of the original vector regardless the coordinates system.

[@raulbeienheimer]

So the Transition Matrix is a Linear Map, right?

[@raulbeienheimer]

*I think I was wrong, it is actually a Bilinear Form, since the basis column vectors are orthogonal; correct?

[@WrathofMath]

We will generally view it as a linear transformation, as it satisfies the linearity properties of additivity and homogeneity. But it is also a bilinear form under the view of it being a function acting on two coordinates, rather than a matrix transforming a vector.