Linear Algebra
线性代数是人工智能与机器学习的数学基石，研究向量空间、矩阵、线性变换及其应用。课程内容包括行列式、矩阵运算、线性方程组、向量空间、特征值与特征向量、二次型、奇异值分解等。学生将掌握矩阵分解与降维方法，为后续机器学习、深度学习、计算机视觉等课程的算法推导与实现奠定坚实的数学基础。
Linear Algebra is the mathematical foundation of AI and machine learning, covering vector spaces, matrices, linear transformations, and applications. Topics include determinants, matrix operations, linear equations, vector spaces, eigenvalues and eigenvectors, quadratic forms, and singular value decomposition. Students master matrix decomposition and dimensionality reduction, laying the mathematical groundwork for machine learning, deep learning, and computer vision.
学生需实现基于奇异值分解（SVD）的图像压缩算法。要求对灰度图像进行SVD分解，保留前k个奇异值重构图像，分析压缩比与图像质量的关系。需使用Python或MATLAB实现，绘制不同k值下的重构效果对比图，并撰写实验报告讨论误差与压缩率的权衡。
Students implement an image compression algorithm based on Singular Value Decomposition (SVD). The project requires performing SVD on grayscale images, reconstructing with the top k singular values, and analyzing the trade-off between compression ratio and image quality. Implementation in Python or MATLAB, with comparison plots for different k values and a report discussing error and compression trade-offs.