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I want to test the rank of a matrix, is there someone who can recommend a package/function in R for this?
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If we have a matrix with dimensions R x C, having R number of rows and C number of columns, and if R is less than C then the rank of the matrix would be R. To find the rank of a matrix in R, we can use rankMatrix function in Matrix package.
The maximum number of linearly independent vectors in a matrix is equal to the number of non-zero rows in its row echelon matrix. Therefore, to find the rank of a matrix, we simply transform the matrix to its row echelon form and count the number of non-zero rows.
The rank of a matrix is the dimension of the subspace spanned by its rows. As we will prove in Chapter 15, the dimension of the column space is equal to the rank. This has important consequences; for instance, if A is an m × n matrix and m ≥ n, then rank (A) ≤ n, but if m < n, then rank (A) ≤ m.
You can try the function qr ("qr", because it performs a QR decomposition):
#define a matrix for this example M <- matrix(data = rnorm(12), ncol = 3) #run the function qr() qr(M)$rank #Alternative: load the Matrix package... require(Matrix) #...and run the function rankMatrix() rankMatrix(M)[1] If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
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