如何找到R中矩阵的秩？
矩阵的秩" title="矩阵的秩">矩阵的秩定义为行或列中线性独立向量的最大数量。如果我们有一个矩阵，其尺寸为R x C，具有R行数和C列数，并且如果R小于C，则矩阵的秩为R。要找到R中矩阵的秩，我们可以在Matrix包中使用rankMatrix函数。
加载矩阵包-
library(Matrix)
示例
M1<-matrix(1:9,ncol=3)M1
输出结果
[,1] [,2] [,3][1,] 1 4 7
[2,] 2 5 8
[3,] 3 6 9
rankMatrix(M1)[1] [1] 2
示例
M2<-matrix(1:36,nrow=6)M2
输出结果
[,1] [,2] [,3] [,4] [,5] [,6][1,] 1 7 13 19 25 31
[2,] 2 8 14 20 26 32
[3,] 3 9 15 21 27 33
[4,] 4 10 16 22 28 34
[5,] 5 11 18 24 30 36
rankMatrix(M2)[1] [1] 2
示例
M3<-matrix(sample(0:9,100,replace=TRUE),nrow=20)M3
输出结果
[,1] [,2] [,3] [,4] [,5][1,] 9 8 1 4 1
[2,] 5 3 0 6 1
[3,] 2 6 5 5 4
[4,] 5 8 3 7 5
[5,] 3 1 4 0 3
[6,] 1 5 5 3 5
[7,] 0 3 0 3 5
[8,] 1 9 4 0 4
[9,] 1 4 3 7 6
[10,] 1 3 6 1 4
[11,] 6 9 2 5 9
[12,] 7 0 2 8 1
[13,] 5 9 4 1 1
[14,] 9 1 1 6 4
[15,] 1 4 4 0 7
[16,] 6 0 9 2 7
[17,] 9 3 0 2 1
[18,] 9 6 0 7 2
[19,] 5 2 0 8 5
[20,] 8 8 4 0 4
rankMatrix(M3)[1] [1] 5
示例
M4<-matrix(sample(21:50,160,replace=TRUE),nrow=20)M4
输出结果
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8][1,] 49 35 25 36 31 22 49 42
[2,] 45 33 21 39 37 26 41 37
[3,] 36 30 46 50 26 32 24 49
[4,] 33 39 31 39 37 50 50 32
[5,] 41 38 39 38 40 25 42 30
[6,] 34 49 26 34 24 34 42 26
[7,] 40 44 30 21 27 47 32 47
[8,] 35 27 21 25 37 28 48 27
[9,] 34 50 41 38 39 27 43 40
[10,] 21 41 50 28 32 38 22 25
[11,] 26 46 34 29 24 38 28 39
[12,] 36 41 36 47 49 48 49 31
[13,] 44 50 37 38 33 26 37 45
[14,] 31 22 47 37 47 41 23 45
[15,] 42 39 38 26 35 21 31 31
[16,] 50 29 40 47 48 34 23 29
[17,] 49 21 30 47 24 21 43 47
[18,] 27 22 25 34 45 28 49 45
[19,] 38 39 32 31 29 23 34 45
[20,] 45 37 31 43 40 27 29 36
rankMatrix(M4)[1] [1] 8
示例
M5<-matrix(sample(rnorm(20),25,replace=TRUE),nrow=5)M5
输出结果
[,1] [,2] [,3] [,4] [,5][1,] 0.73475325 -1.2186186 -0.21496111 1.8642877 1.1133489
[2,] -0.09091262 -0.4513579 0.18346741 0.1834674 -0.4513579
[3,] 1.55003168 -0.1454168 0.28244025 0.5674004 1.5706586
[4,] -0.90693971 -1.2186186 -0.09091262 -0.1454168 1.0289755
[5,] -0.45135792 0.5674004 0.28244025 -0.2149611 1.5500317
rankMatrix(M5)[1] [1] 5
示例
M6<-matrix(sample(rexp(5,2),20,replace=TRUE),nrow=10)M6
输出结果
[,1] [,2][1,] 0.2969787 3.5003481
[2,] 0.5462926 3.5003481
[3,] 1.0018821 0.5462926
[4,] 3.5003481 0.2969787
[5,] 1.0018821 0.2969787
[6,] 1.0018821 0.2969787
[7,] 1.0018821 0.5462926
[8,] 0.2133455 0.2133455
[9,] 0.5462926 3.5003481
[10,] 0.2969787 0.2133455
rankMatrix(M6)[1] [1] 2
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