> Would it be possible to develop a computer from linear transformations?
Yes. The transition function of Turing machines and the working tape can be represented as linear transformations. For quantum computers, these transformations even need to be unitary.
This very standard construction does not conflict with the halting problem: you don't know how often you have to apply this linear transform to your state vector until you got your result.
Yes. The transition function of Turing machines and the working tape can be represented as linear transformations. For quantum computers, these transformations even need to be unitary.
This very standard construction does not conflict with the halting problem: you don't know how often you have to apply this linear transform to your state vector until you got your result.