TensorFlow

TensorFlow - 矩阵

flyfish

矩阵

A=⎡⎣⎢−1.320.49.70.65.5−6.2⎤⎦⎥

A=⎡⎣⎢⎢⎢⎢⎢a11a21⋮am1a12a22⋮am2⋯⋯⋱⋯a1na2n⋮amn⎤⎦⎥⎥⎥⎥⎥=⎛⎝⎜⎜⎜⎜⎜a11a21⋮am1a12a22⋮am2⋯⋯⋱⋯a1na2n⋮amn⎞⎠⎟⎟⎟⎟⎟=(aij)∈Rm×n.

单位矩阵(identity matrix, 有时候不确切的叫unit matrix)

I1=[1], I2=[1001], I3=⎡⎣⎢100010001⎤⎦⎥, ⋯, In=⎡⎣⎢⎢⎢⎢⎢⎢⎢100⋮0010⋮0001⋮0⋯⋯⋯⋱⋯000⋮1⎤⎦⎥⎥⎥⎥⎥⎥⎥

矩阵加法（Matrix addition）

A+B=⎡⎣⎢⎢⎢⎢⎢a11a21⋮am1a12a22⋮am2⋯⋯⋱⋯a1na2n⋮amn⎤⎦⎥⎥⎥⎥⎥+⎡⎣⎢⎢⎢⎢⎢b11b21⋮bm1b12b22⋮bm2⋯⋯⋱⋯b1nb2n⋮bmn⎤⎦⎥⎥⎥⎥⎥=⎡⎣⎢⎢⎢⎢⎢a11+b11a21+b21⋮am1+bm1a12+b12a22+b22⋮am2+bm2⋯⋯⋱⋯a1n+b1na2n+b2n⋮amn+bmn⎤⎦⎥⎥⎥⎥⎥

矩阵乘法（Matrix multiplication)

1 Row vector 和 column vector相乘
A=(abc),B=⎛⎝⎜xyz⎞⎠⎟,

AB=(abc)⎛⎝⎜xyz⎞⎠⎟=ax+by+cz,

BA=⎛⎝⎜xyz⎞⎠⎟(abc)=⎛⎝⎜xayazaxbybzbxcyczc⎞⎠⎟.

2 Square matrix 和 column vector 相乘

A=⎛⎝⎜apubqvcrw⎞⎠⎟,B=⎛⎝⎜xyz⎞⎠⎟,

AB=⎛⎝⎜apubqvcrw⎞⎠⎟⎛⎝⎜xyz⎞⎠⎟=⎛⎝⎜ax+by+czpx+qy+rzux+vy+wz⎞⎠⎟,

BA没有定义

3 square matrix和square matrix相乘
matrix的复数是metrices

A=⎛⎝⎜apubqvcrw⎞⎠⎟,B=⎛⎝⎜αλρβμσγντ⎞⎠⎟,

AB=⎛⎝⎜apubqvcrw⎞⎠⎟⎛⎝⎜αλρβμσγντ⎞⎠⎟=⎛⎝⎜aα+bλ+cρpα+qλ+rρuα+vλ+wρaβ+bμ+cσpβ+qμ+rσuβ+vμ+wσaγ+bν+cτpγ+qν+rτuγ+vν+wτ⎞⎠⎟,

BA=⎛⎝⎜αλρβμσγντ⎞⎠⎟⎛⎝⎜apubqvcrw⎞⎠⎟=⎛⎝⎜αa+βp+γuλa+μp+νuρa+σp+τuαb+βq+γvλb+μq+νvρb+σq+τvαc+βr+γwλc+μr+νw;ρc+σr+τw⎞⎠⎟.

代码

VC++下编译
库Eigen

typedef Matrix< double , 2 , 2 > Matrix2dMatrix<double, 2, 2>  是定义一个2×2的矩阵，矩阵元素以double类型存储

配置

#include "stdafx.h"#include <iostream>#include "Eigen\Dense"int main(){    Eigen::Matrix2d a;    a << 1, 2,         3, 4;    Eigen::MatrixXd b(2, 2);    b << 5, 6,         7, 8;    std::cout << "a + b =\n" << a + b << "\n"<< std::endl;    std::cout << "a * b =\n" << a * b << std::endl;    system("pause");    return 0;}

输出