Question

如何在R中找到矩阵的符号反转;例如：

Matrix.test <- function(x) matrix(c(x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, 2*x, 3*x, 4*x, 2*x^2, 3*x^3, 4*x^4, 5*x^5), 4, 4)

我知道有一个名为'Ryacas'的包，它是'yacas'的接口，但是我不能用它来做这样的计算。 'yacas'是一个用于符号操纵数学表达式的程序。有关详细信息，请参阅link。

谢谢

Answer 1

它适用于我：

> library(Ryacas)
> x <- Sym('x')
> M <- List(List(1,x),List(x,1))
> PrettyForm(M)
/              \
| ( 1 ) ( x )  |
|              |
| ( x ) ( 1 )  |
\              /
> PrettyForm(Inverse(M))
/                        \
| /   1    \ / -( x ) \  |
| | ------ | | ------ |  |
| |      2 | |      2 |  |
| \ 1 - x  / \ 1 - x  /  |
|                        |
| / -( x ) \ /   1    \  |
| | ------ | | ------ |  |
| |      2 | |      2 |  |
| \ 1 - x  / \ 1 - x  /  |
\                        /

Answer 2

接下来：

M2 <- List(List(  x,     x^2,  x^3,  x^4),
           List(  x^5,   x^6,  x^7,  x^8),
           List(  x^9, 2*x  ,3*x  ,  4*x),
           List(2*x^2, 3*x^3, 4*x^4, 5*x^5))
Inverse(M2)

但答案非常复杂（我只能为重新格式化前四行而烦恼）：

{{(x^6*3*x*5*x^5-x^6*4*x*4*x^4+x^8*2*x*4*x^4-x^7*2*x*5*x^5+
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   x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+
   x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-
   x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2),(x^4*3*x*3*x^3-x^4*2*x*4*x^4+x^3*2*x*5*x^5-x^3*4*x*3*x^3-x^2*3*x*5*x^5+x^2*4*x*4*x^4)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2),0,(x^10*3*x-x^9*4*x-x^10*3*x+x^9*4*x-x^11*2*x+x^11*2*x)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2)},{(x^5*4*x*4*x^4-x^5*3*x*5*x^5-x^17*4*x^4+x^16*5*x^5-x^7*4*x*2*x^2+x^8*3*x*2*x^2)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2),(3*x^2*5*x^5-4*x^2*4*x^4+x^13*4*x^4-x^4*3*x*2*x^2-x^12*5*x^5+x^3*4*x*2*x^2)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2),0,(x^8*4*x-x^9*3*x+x^9*3*x-x^8*4*x)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2)},{(x^5*2*x*5*x^5-x^5*4*x*3*x^3+x^17*3*x^3-x^15*5*x^5+x^6*4*x*2*x^2-x^8*2*x*2*x^2)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2),(4*x^2*3*x^3-2*x^2*5*x^5-x^13*3*x^3+x^11*5*x^5-x^2*4*x*2*x^2+x^4*2*x*2*x^2)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2),(x^7*5*x^5-x^9*3*x^3+x^9*3*x^3-x^7*5*x^5)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2),(x^9*2*x-x^7*4*x-x^9*2*x+x^7*4*x-x^19+x^19)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2)},{(x^5*3*x*3*x^3-x^5*2*x*4*x^4-x^16*3*x^3+x^15*4*x^4-x^6*3*x*2*x^2+x^7*2*x*2*x^2)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2),(2*x^2*4*x^4-3*x^2*3*x^3+x^12*3*x^3-x^11*4*x^4+x^2*3*x*2*x^2-x^3*2*x*2*x^2)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2),(x^8*3*x^3-x^7*4*x^4-x^8*3*x^3+x^7*4*x^4-x^9*2*x^2+x^9*2*x^2)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2),(x^7*3*x-x^8*2*x+x^8*2*x-x^7*3*x)/(x^7*3*x*5*x^5-x^7*4*x*4*x^4-x^8*2*x*5*x^5+x^8*4*x*3*x^3-x^9*3*x*3*x^3+x^9*3*x*3*x^3+x^8*2*x*5*x^5-x^8*4*x*3*x^3-x^7*3*x*5*x^5+x^7*4*x*4*x^4-x^19*4*x^4+x^19*4*x^4+x^18*5*x^5-x^9*4*x*2*x^2-x^18*5*x^5+x^9*4*x*2*x^2-x^11*2*x*2*x^2+x^11*2*x*2*x^2)}};

R中矩阵的符号逆

2 个答案: