Plane computer graphics are basic information carriers in many industrial scenarios, such as engineering simulation, automatic control, and software design. Plane computer graphics are generally a kind of digital signals guided by mathematical symbols, and each vertex of a plane computer graph forms a graph matrix. Therefore, linear matrix transformation serves as the most common algorithmic unit to realize various information processing operations. To improve ease of graph matrix computing in practical engineering scenarios, this paper proposes a theoretical scientific programming framework for application of linear matrix transformation in plane computer graphics. Firstly, theoretical basis of linear matrix transformation in homogeneous plane coordinates is displayed and analyzed. Then, the universal theorem about linear transformation of graph matrices is deduced, and corresponding proofs are also given. Finally, a case study is set up to demonstrate the main workflow of the proposed theoretical scientific programming framework. The simulative results reveal feasibility of the proposal.