title: [线性代数]6-2:对角化(Diagonalizing a Matrix) categories: Mathematic Linear Algebra keywords: Eigenvalues Eigenvectors Diagonalizing Fibonacci Numbers AkA^kAk Nondiagonalizable Matrix toc: true date: 2017-11-21 11:48:42 Abstract: 矩阵对角化,以及对角化过程中引入的知识,以…

title: [线性代数]7-3:对角化和伪逆(Diagonalization and the Pseudoinverse) categories: Mathematic Linear Algebra keywords: Diagonalization Pseudoinverse toc: true date: 2017-12-06 14:03:08 Abstract: 本文以线性变换的角度重新理解矩阵变换的原理,以对角化和SVD作为主要的案例 Keywords: Diagonalization…

手动博客搬家: 本文发表于20181212 09:37:21, 原地址https://blog.csdn.net/suncongbo/article/details/84962727 呜啊怎么又是数学了啊...数学比例\(\frac{16}{33}=0.4848\) orz yhx-12243神仙 题目链接: https://codeforces.com/contest/947/problem/E 题意: 有一个\([0,n]\)的随机数\(x\)初始为\(i\)的概率为\(p_i\). \(m…

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Today we have learned the Matrix Factorization, and I want to record my study notes. Some kownledge which I have learned before is forgot...(呜呜) 1.Terminology 单位矩阵:identity matrix 特征值:eigenvalues 特征向量:eigenvectors 矩阵的秩:rank 对角矩阵:diagonal matrix 对角化矩阵…

torch.mul() 函数功能:逐个对 input 和 other 中对应的元素相乘. 本操作支持广播,因此 input 和 other 均可以是张量或者数字. 举例如下: >>> import torch >>> a = torch.randn(3) >>> a tensor([-1.7095, 1.7837, 1.1865]) >>> b = 2 >>> torch.mul(a, b) tensor([-3.4…

利用特征向量的属性,矩阵 \(A\) 可以变成一个对角化矩阵 \(\Lambda\). 1. 对角化 假设一个 \(n×n\) 的矩阵 \(A\) 有 \(n\) 个线性不相关的特征向量 \(x_1,\cdots,x_n\) ,把它们作为特征向量矩阵 \(S\) 的列,那么就有 \(S^{-1}AS=\Lambda\). 矩阵 \(A\) 被对角化了,因为所有的特征向量位于矩阵 \(\Lambda\)的对角线上. 证明过程也很简单,首先我们计算 \(AS\). 一个技巧就是将 \(AS\) 分解…

Matrix factorization 导语:承载上集的矩阵代数入门,今天来聊聊进阶版,矩阵分解.其他集数可在[线性代数]标籤文章找到.有空再弄目录什麽的. Matrix factorization is quite like an application of invertible matrices, where L is an invertible matrix in LU factorization. As you may have seen, that solving Ax=b for…

title: [线性代数]7-2:线性变化的矩阵(The Matrix of a Linear Transformation) categories: Mathematic Linear Algebra keywords: Matrix Matrix for the Derivate Matrix for the Integral Construction of the Matrix ABABAB Match TSTSTS Multiplication Change of Basis Matri…

title: [线性代数]2-3:消元与矩阵的关系(Elimination and Matrix) toc: true categories: Mathematic Linear Algebra date: 2017-08-31 17:55:10 keywords: Elimination Matrix Matrix Multiplication Row Exchange Augmented Matrix Abstract: 用大学的方法消元,也就是整个消元过程矩阵化,引出矩阵乘法 Keywor…