# Inverse of higher order matrix

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raina RAJ on 9 Feb 2021
Answered: Christine Tobler on 10 Feb 2021
Hello there,
I am trying to get inverse of a 80,000 order matrix but the calculation is taking too much time. Is there any fastest way or method to calculate the inverse of a matrix?
raina RAJ on 10 Feb 2021
Yes matrix Q is stored in sparse data format and e is ones(M,1).

Matt J on 10 Feb 2021
Edited: Matt J on 10 Feb 2021
I have system of equations xQ = 0 and xe =1 where 'e' is a column vector of appropriate dimension, x is a row vector of size (1,M) and Q matix has size (M,M).
If Q is sparse, you can do,
x=eigs(Q.',1,'sm');
x=x/sum(x);

Christine Tobler on 10 Feb 2021
Another way of looking at the equations x*Q = 0 and x e = 1 is as an equation system x * [Q e] = [0 1], which you could solve using
A = [Q, ones(n, 1)]';
b = [zeros(n, 1); 1];
x = A \ b;
or if this is too slow, you could try an iterative algorithm:
x = lsqr(A, b);

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