矩阵的行列式, 指正方矩阵的行列式.
计算方法参考 :
如图 :
2阶矩阵的行列式
3阶矩阵的行列式
在R中使用det可以迅速的得到矩阵的行列式的值.
需要注意矩阵必须是正方矩阵.
[参考]
> x <- matrix(1:12,3,4)
> x
[,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
> det(x)
Error in determinant.matrix(x, logarithm = TRUE, ...) :
'x' must be a square matrix
> x <- matrix(1:16,4,4)
> det(x)
[1] 0
> x
[,1] [,2] [,3] [,4]
[1,] 1 5 9 13
[2,] 2 6 10 14
[3,] 3 7 11 15
[4,] 4 8 12 16
> det(t(x))
[1] 4.733165e-30
> t(x)
[,1] [,2] [,3] [,4]
[1,] 1 2 3 4
[2,] 5 6 7 8
[3,] 9 10 11 12
[4,] 13 14 15 16[参考]
1.
http://zh.wikipedia.org/wiki/%E8%A1%8C%E5%88%97%E5%BC%8F
2. > help(det)
det package:base R Documentation
Calculate the Determinant of a Matrix
Description:
‘det’ calculates the determinant of a matrix. ‘determinant’ is a
generic function that returns separately the modulus of the
determinant, optionally on the logarithm scale, and the sign of
the determinant.
Usage:
det(x, ...)
determinant(x, logarithm = TRUE, ...)
Arguments:
x: numeric matrix: logical matrices are coerced to numeric.
logarithm: logical; if ‘TRUE’ (default) return the logarithm of the
modulus of the determinant.
...: Optional arguments. At present none are used. Previous
versions of ‘det’ allowed an optional ‘method’ argument.
This argument will be ignored but will not produce an error.
Details:
The ‘determinant’ function uses an LU decomposition and the ‘det’
function is simply a wrapper around a call to ‘determinant’.
Often, computing the determinant is _not_ what you should be doing
to solve a given problem.
Value:
For ‘det’, the determinant of ‘x’. For ‘determinant’, a list with
components
modulus: a numeric value. The modulus (absolute value) of the
determinant if ‘logarithm’ is ‘FALSE’; otherwise the
logarithm of the modulus.
sign: integer; either +1 or -1 according to whether the determinant
is positive or negative.
Examples:
(x <- matrix(1:4, ncol = 2))
unlist(determinant(x))
det(x)
det(print(cbind(1, 1:3, c(2,0,1))))
