r - R中矩阵的符号逆

Question

如何在 R 中找到矩阵的符号逆；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，但我无法应用它来进行此类计算。'yacas' 是一个用于对数学表达式进行符号操作的程序。请参阅链接了解更多详情。

谢谢你

Answer 1

这对我来说可以：

> 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

并遵循：

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)

不过，答案相当复杂（我只能费心重新格式化前四行）：

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