CODEWITHSUNDEEP
wolfram-mathematicalinear-algebra
zhjzwlys
zhjzwlys

Reputation: 11

Check whether a system of linear equations has a a solution

What is the fastest way to check whether a system of linear equations has a solution?

All numbers are rational numbers and the (large) coefficient matrix can be given in the form of SparseArray.

I know that LinearSolve can solve this problem, but if you don't need to know what the solution is, but only need to judge the existence, is there a more efficient method?

The way to calculate rank seems to be slower when there is no solution.

By the way, when I use 'LinearSolve', the form of 'SparseArray' can't help me get faster, even if there are only very limited non-zero elements in each row.

Upvotes: 1

Views: 113

Answers (1)

Meng Lu
Meng Lu

Reputation: 14637

One idea is verifying

Det[PseudoInverse[m]] == 0.

where m is the square matrix of the coefficients.

Upvotes: 0

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