李老师的《矩阵分析与应用》，大作业，不要照搬以免被判挂科。保存此案例以便测试程序、科研创新调用。 完成课堂上讲的关于矩阵分解的LU分解、QR分解（Gram-Schmidt）、Orthogonal Reduction (Householder变换 reduction 和Givens变换 reduction)和 URV程序实现。在此基础上 ...

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这项由北京大学高可信软件技术教育部重点实验室刘伟领导的研究团队发表于2025年12月的arXiv预印本论文，编号为2512.22469v1，展示了一种全新的软件问题定位方法。字节跳动的彭超和高鹏飞等研究人员也参与了这项研究。有兴趣深入了解技术细节的读者可以通过论文编号arXiv:2512.22469v1查询完整论文。 想象一下，当你的电脑软件出现问题时，程序员就像医生一样，需要根据你描述的"症状" ...

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