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I think what is missing here is a concrete math proof.

I came across this on the coursera website, see this link.

Watch from 10:40 till the end. I think it clearly explains ( taken from the above answer by @tbh )

"When referring to transform between coordinate frames (transforming the frames, it is the inverse of the transform of data between the two frames)"

I think what is missing here is a concrete math proof.

I came across this on the coursera website, see this link.

Watch from 10:40 till the end. I think

Read this after watching the above video once -

The video explains how to get source datapoint using the Rotation Matrix. The opposite ( by taking a simple transpose of Rotation matrix ) is true for getting the target data point in the source frame, you have to use the inverse of the Rotation matrix ( Rotation required to convert source to target basis vectors )

Hence it clearly also explains ( taken from the above answer by @tbh )

"When referring to transform between coordinate frames (transforming the frames, it is the inverse of the transform of data between the two frames)"