首页 > 编程知识 正文

矩阵求det的公式,行列式值det的公式

时间:2023-05-03 23:17:45 阅读:285887 作者:3397

矩阵的行列式, 指正方矩阵的行列式. 计算方法参考 :  http://zh.wikipedia.org/wiki/%E8%A1%8C%E5%88%97%E5%BC%8F 如图 :   对于简单的2阶和3阶的矩阵,行列式的表达式相对简单,而且恰好是每条主对角线(左上至右下)元素乘积之和减去每条副对角线(右上至左下)元素乘积之和(见图中红线和蓝线)。 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.
> 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 DocumentationCalculate the Determinant of a MatrixDescription: ‘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))))

版权声明:该文观点仅代表作者本人。处理文章:请发送邮件至 三1五14八八95#扣扣.com 举报,一经查实,本站将立刻删除。