matrix-inverse

I am finding it very hard to understand the way the inverse of the matrix is calculated in the Hill Cipher algorithm. I get the idea of it all being done in modulo arithmetic, but somehow things are not adding up. I would really appreciate a simple explanation! Consider the following Hill Cipher key matrix: 5 8 17 3 Please use the above matrix for illustration. You must study the Linear congruence theorem and the extended GCD algorithm , which belong to Number Theory , in order to understand the maths behind modulo arithmetic . The inverse of matrix K for example is (1/det(K)) * adjoint(K),

I am working with data from neuroimaging and because of the large amount of data, I would like to use sparse matrices for my code (scipy.sparse.lil_matrix or csr_matrix). In particular, I will need to compute the pseudo-inverse of my matrix to solve a least-square problem. I have found the method sparse.lsqr, but it is not very efficient. Is there a method to compute the pseudo-inverse of Moore-Penrose (correspondent to pinv for normal matrices). The size of my matrix A is about 600'000x2000 and in every row of the matrix I'll have from 0 up to 4 non zero values. The matrix A size is given by

I was wondering what is your recommended way to compute the inverse of a matrix? The ways I found seem not satisfactory. For example, > c=rbind(c(1, -1/4), c(-1/4, 1)) > c [,1] [,2] [1,] 1.00 -0.25 [2,] -0.25 1.00 > inv(c) Error: could not find function "inv" > solve(c) [,1] [,2] [1,] 1.0666667 0.2666667 [2,] 0.2666667 1.0666667 > solve(c)*c [,1] [,2] [1,] 1.06666667 -0.06666667 [2,] -0.06666667 1.06666667 > qr.solve(c)*c [,1] [,2] [1,] 1.06666667 -0.06666667 [2,] -0.06666667 1.06666667 Thanks! solve(c) does give the correct inverse. The issue with your code is that you are using the wrong

updated on this question: I have closed this question and I will post a new question focus on R package Rmpfr. To conclude this question and to help others, I will post my codes of the inverse of a Vandermonde Matrix from its explicit inverse formula. The generation terms are the x's in [here] 1 . I am not a skilled programmer. Therefore I don't expect my codes to be the most efficient one. I post the codes here because it is better than nothing. library(gtools) #input is the generation vector of terms of Vandermonde matrix. FMinv <- function(base){ n=length(base) inv=matrix(nrow=n,ncol=n) for

this is my solving process from the exercise of [a beginner's guide to R] > Q [,1] [,2] [,3] [1,] 1 2 3 [2,] 4 2 1 [3,] 2 3 0 > solve(Q) [,1] [,2] [,3] [1,] -0.12 0.36 -0.16 [2,] 0.08 -0.24 0.44 [3,] 0.32 0.04 -0.24 > solve(Q)%*%Q [,1] [,2] [,3] [1,] 1 -2.775558e-17 0 [2,] 0 1.000000e+00 0 [3,] 0 0.000000e+00 1 I wonder why I cannot get to the right answer that the identity matrix should come out. Use the zapsmall function on the final result. Due to floating point representation and rounding errors anything more than simple arithmatic (and even that sometimes) will result in values that are