Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Why is the trace preserving part necessary? Is it not enough if it can take all matrices to matrices of trace 1?
Those maps are linear, so if it preserves the trace of trace 1 matrices then it preserves the trace of any other matrix.
We just don't need to restrict ourselves by considering only trace 1 matrices (from mathematical point of view).
Required, but never shown