如何计算R中矩阵的零空间，以使所得的矢量根据R中的自由变量显示基本变量? [英] How to calculate null space of a matrix in R so that the resulting vectors show basic variables in terms of free variables in R?

问题描述

我有一个矩阵A1，我想计算它的空空间.

I have a matrix A1 and I want to calculate it's null space.

A1=matrix(c(1,1,2,3,2,1,1,3,1,4),nrow=2,ncol=5,byrow =TRUE)



    [,1] [,2] [,3] [,4] [,5]
[1,]    1    1    2    3    2
[2,]    1    1    3    1    4

我从软件包'pracma'中使用了'nullspace'函数.

I have using the function 'nullspace' from the package 'pracma'.

nullspace(matrix(c(1,1,2,3,2,1,1,3,1,4),nrow=2,ncol=5,byrow =TRUE))

我得到的结果是

            [,1]        [,2]       [,3]
[1,] -0.53530338 -0.53530338 -0.6117753
[2,]  0.23344278 -0.76655722  0.5525060
[3,]  0.68910778  0.02244112 -0.4505435
[4,] -0.07744944  0.25588390  0.1019625
[5,] -0.42200333  0.24466334  0.3272343

但是当我手动解决它时，我得到的结果是

But when I am solving it manually, the result I am getting is

            [,1]        [,2]       [,3]
[1,]         -1          -7          2
[2,]          1           0          0
[3,]          0           2         -2
[4,]          0           1          0
[5,]          0           0          1

如何使用R代码获得第二个答案? 我找不到任何包装.

How can I get the second answer using R codes? I cant find any package for this.

推荐答案

请仔细阅读此问题与解答；答:解决R中任何m * n矩阵A的同质系统Ax = 0(找到A的零空间基础).

Have a close read on this Q & A: Solve homogenous system Ax = 0 for any m * n matrix A in R (find null space basis for A).

答案中的NullSpace函数完全符合您的期望.

The NullSpace function in the answer does exactly what you are look for.

## Your matrix
A1 <- matrix(c(1,1,2,3,2,1,1,3,1,4),nrow=2,ncol=5,byrow =TRUE)

## get NullSpace from the linked Q & A yourself

## call NullSpace
X <- NullSpace(A1)

round(X, 15)
#     [,1] [,2] [,3]
#[1,]   -7    2   -1
#[2,]    0    0    1
#[3,]    2   -2    0
#[4,]    1    0    0
#[5,]    0    1    0

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