How to find Rank of a Matrix in R

How to find Rank of a Matrix in R ?

Answer

To find the rank of a matrix in R, you can use the qr() function followed by the qr.R() function, and then count the number of non-zero rows in the resulting upper triangular matrix.


✐ Examples

1 Find Rank of a 2x2 Matrix

In this example,

  1. First, we create a 2x2 matrix named matrix1 using the matrix() function with a vector of values c(1, 2, 3, 4) and specify the number of rows as 2.
  2. We use the qr() function on matrix1 to perform QR decomposition and store the result in a variable called qr1.
  3. Next, we extract the upper triangular matrix R from the QR decomposition result using the qr.R() function on qr1.
  4. To find the rank, we count the number of non-zero rows in the upper triangular matrix. This can be done by summing the logical values of whether the absolute values of the diagonal elements of R are greater than a small tolerance value (e.g., .Machine$double.eps).
  5. Finally, we print the rank of the matrix.

R Program

matrix1 <- matrix(c(1, 2, 3, 4), nrow = 2)
qr1 <- qr(matrix1)
R1 <- qr.R(qr1)
rank1 <- sum(abs(diag(R1)) > .Machine$double.eps)
print(rank1)

Output

[1] 2

2 Find Rank of a 3x3 Matrix

In this example,

  1. We first create a 3x3 matrix named matrix2 using the matrix() function with a vector of values c(1, 2, 3, 4, 5, 6, 7, 8, 9) and specify the number of rows as 3.
  2. We use the qr() function on matrix2 to perform QR decomposition and store the result in a variable called qr2.
  3. Next, we extract the upper triangular matrix R from the QR decomposition result using the qr.R() function on qr2.
  4. To find the rank, we count the number of non-zero rows in the upper triangular matrix. This can be done by summing the logical values of whether the absolute values of the diagonal elements of R are greater than a small tolerance value (e.g., .Machine$double.eps).
  5. Finally, we print the rank of the matrix.

R Program

matrix2 <- matrix(c(1, 2, 3, 4, 5, 6, 7, 8, 9), nrow = 3)
qr2 <- qr(matrix2)
R2 <- qr.R(qr2)
rank2 <- sum(abs(diag(R2)) > .Machine$double.eps)
print(rank2)

Output

[1] 2

3 Find Rank of a 3x3 Identity Matrix

In this example,

  1. First, we create a 3x3 identity matrix named matrix3 using the diag() function with a value of 3.
  2. We use the qr() function on matrix3 to perform QR decomposition and store the result in a variable called qr3.
  3. Next, we extract the upper triangular matrix R from the QR decomposition result using the qr.R() function on qr3.
  4. To find the rank, we count the number of non-zero rows in the upper triangular matrix. This can be done by summing the logical values of whether the absolute values of the diagonal elements of R are greater than a small tolerance value (e.g., .Machine$double.eps).
  5. Finally, we print the rank of the matrix.

R Program

matrix3 <- diag(3)
qr3 <- qr(matrix3)
R3 <- qr.R(qr3)
rank3 <- sum(abs(diag(R3)) > .Machine$double.eps)
print(rank3)

Output

[1] 3

Summary

In this tutorial, we learned How to find Rank of a Matrix in R language with well detailed examples.


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