摘要：线性代数是一门重要的数学课程，它主要讲授向量、矩阵和相关的计算方法。它能够帮助我们理解和探索复杂问题的内在本质，也能帮助我们将不同学科之间的知识进行融会贯通。本文将介绍如何利用线性代数来实现这一目标，并分享作者的感受和思考。 关键词： 线性代数； 融会贯通； 向量 ； 矩阵 Introduction: Linear algebra is an important mathematics course which mainly teaches vectors, matrices and related computation methods. It can help us to understand and explore the inner essence of complex problems, and also help us to integrate knowledge between different disciplines. In this paper, we will introduce how to use linear algebra to achieve this goal, and share the author's feelings and thoughts. Body: Linear algebra is a powerful tool for interdisciplinary integration because it can be used to analyze data from different fields in a unified way. For example, in physics, we can use linear algebra to study the motion of particles by analyzing the vector equation; in economics, we can use linear algebra to analyze market trends by studying matrix equations; in computer science, we can use linear algebra to solve optimization problems by studying matrix operations. All these applications show that linear algebra provides a unified framework for understanding different fields of knowledge. Besides its application in different fields of knowledge, linear algebra also has great practical value. For example, it can be used for data analysis or machine learning tasks such as classification or regression tasks. By using matrix operations and other tools provided by linear algebra, we can obtain more accurate results than traditional methods such as statistical analysis or manual calculation. This shows that linear algebra not only helps us understand abstract concepts but also provides practical solutions for real-world problems. Conclusion: In conclusion, through this paper we have seen how powerful toollinearalgebraisforinterdisciplinaryintegrationandreal-worldproblemsolvingtasks .It helpsusunderstandtheinneressenceofcomplexproblemsandprovidesaunifiedframeworkforunderstandingdifferentfields ofknowledge .Moreover ,it has greatpracticalvaluein dataprocessingandmachinelearningtasks .Itisindeedanessentialtoolforourmodernsociety .