One, create a vector
1. In R, you can use the function c() to create a vector
x1=c(171,175,159,155,152,160)
y1=c(57,64,41,38,35,40)
2. In R, you can use the function length() to view the vector length
length(x1)
3. In R, you can use the function mode() to view the data type
mode(x1)
4. R language uses ":" to quickly generate arithmetic sequence
a = 1:12
a
b = c(1,3,6:4,9)
b
Two, create a matrix
(1) The x1 and y1 are all row vectors, which can also be regarded as a matrix with 1 row and 12 columns
1. R language uses matrix() to create a matrix
matrix(data = NA,nrow = 1,ncol = 1,byrow = FALSE,dimnames = NULL) #default value of each parameter
The data item is a necessary matrix element.
nrow is the number of rows.
ncol is the number of columns
. The product of nrow and ncol should be the number of matrix elements. The
byrow item controls whether to arrange the elements in rows or not
dimnames give the names of rows and columns.
A = matrix(c(1,4,2,5,3,6),nrow=2,ncol=3);
print(A)
B = matrix(c(1,2,3,4,5,6),3,2)
print(B)
C = matrix(x1,2,3)
print(C)
D = matrix(x1,3,2)
print(D)
E = matrix(x1,3,2,byrow = T) #创建按行排列的矩阵
print(E)
Three, matrix transpose
1. R language uses t() or transpose() to transpose the matrix
print(A)
print(t(A))
Four, matrix addition and subtraction
R can only add and subtract matrices with the same column in the same row
1. The R language uses "+" to add operations to the same column of the matrix
print(A[,1:2])
print(B[1:2,])
print(A[,1:2] + B[1:2,])
2. R language uses "-" to subtract matrices in the same column
print(A[,1:2])
print(B[1:2,])
print(A[,1:2] - B[1:2,])
Five, matrix multiplication
When A is m * n matrix and B is n * m matrix, the product of A and B can be obtained
1. R language uses "%* %" to multiply matrices
print(A)
print(B)
print(A %*% B)
print(A)
print(B)
print(B %*% A)
Six, the diagonal operation of the matrix
1. The R language uses the diag() function to take the diagonal elements of a square matrix
F = matrix(1:9,3,3)
print(F)
print(diag(F))
2. The R language uses the diag() function to generate a diagonal matrix with the vector in the brackets as diagonal elements. For a positive integer k, a k-dimensional unit vector will be generated
print(diag(diag(F)))
print(diag(4))
Seven, matrix inversion
1. R language uses the solve() function to perform matrix inversion
G = matrix(c(14,32,32,77),2,2)
print(G)
print(solve(G))
R language uses solve(A,b) to solve the linear equations Ax = b. If b is default, the system defaults to the identity matrix, so it can be used for matrix inversion.
Eight, the eigenvalues and vectors of the matrix
1. R language uses eigen() function to find eigenvalues and eigenvectors
eigen(x,symmetric,only.values = FALSE,EISPACK = FALSE)
Among them: x is a matrix, symmetric indicates whether the matrix x is a symmetric matrix, if not specified, the system will automatically monitor whether x is a symmetric matrix
x1=c(17,22,27,22,29,36,27,36,45)
D = matrix(x1,3,3)
print(D)
D.e = eigen(D,symmetric = T)
print(D.e)
Nine, matrix singular value decomposition
1. In R, you can use the svd() function for singular value decomposition
A = matrix(1:18,3,6)
print(A)
A.s = svd(A)
print(A.s)
Ten, the dimension of the matrix
1. Use the dim() function in R to return the dimension of a matrix
A = matrix(1:18,3,6)
print(A)
dim(A)
2. Use the nrow() function in R to return the number of rows of a matrix
A = matrix(1:18,3,6)
print(A)
nrow(A)
3. Use the ncol() function in R to return the number of columns of a matrix
A = matrix(1:18,3,6)
print(A)
ncol(A)
11. Sum of Matrix
1. Use the sum() function in R to sum the elements of the entire matrix
A = matrix(1:18,3,6)
print(A)
sum(A)
2. Use the rowSums() function in R to sum the elements of the matrix row by row
A = matrix(1:18,3,6)
print(A)
rowSums(A)
3. Use the colSums() function in R to sum the elements of the matrix row by row
A = matrix(1:18,3,6)
print(A)
colSums(A)
12. The mean value of the matrix
1. Use the mean() function in R to average the entire matrix,
A = matrix(1:18,3,6)
print(A)
mean(A)
2. Use the rowMeans() function in R to average the matrix by row
A = matrix(1:18,3,6)
print(A)
rowMeans(A)
3. Use the colMeans() function in R to average the matrix by column
A = matrix(1:18,3,6)
print(A)
colMeans(A)