基于深度学习探讨线性代数教学案例设计及应用

Exploring the Design and Application of Linear Algebra Teaching Cases Based on Deep Learning

摘要: 人工智能快速发展的大背景下，迫使作为深度学习理论基础之一的大学线性代数课程教学进行深入的思考。本文基于现有的教学模式进行总结和思考，探讨深度学习与线性代数课程知识点的衔接处，设计理论与实际紧密联系的教学案例，启发学生对知识的探索欲望，感受数学理论知识在当下人工智能发展过程中起到的不可替代的作用。本文主要以矩阵线性运算的教学案例设计为例，通过具体黑白图像和房屋价格预测，形象直观地展示了矩阵运算(特别是矩阵的乘法)在图像和神经网络中的应用，让学生切身感受线性代数的实际应用价值。

Abstract: Amid the rapid development of artificial intelligence, university linear algebra teaching, which serves as a fundamental theoretical component of deep learning, requires thorough re-examination. This paper summarizes and reflects on existing teaching models, explores the connections between deep learning and linear algebra knowledge points, and designs teaching cases that closely integrate theory with practice. These cases aim to stimulate students’ curiosity and help them recognize the indispensable role of mathematical theory in advancing artificial intelligence. Using the instructional design of matrix linear operations as an example, this paper vividly illustrates how matrix operations, particularly matrix multiplication, are applied in image processing and neural networks through concrete examples including grayscale images and house price prediction. This approach enables students to directly appreciate the practical value of linear algebra.