This paper presents a systematic comparison of the curriculum design and application orientation of the linear algebra curriculum in our country and abroad. It explains mainly differences in course objectives, teaching content, approaches, and feedback mechanisms, reflecting divergent understandings of the discipline’s value within distinct educational ecosystems. Forward-looking and practical conclusions are proposed across five main directions: optimizing course structure, strengthening practical components, deepening interdisciplinary integration, building faculty capacity, and developing teaching resources. The aim is to provide strong conceptual help and realistic guidance for getting real progress in linear algebra education in China.