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Determinant of integer matrices

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Rudolf Fruehwirth
Rudolf Fruehwirth 2021-4-23
评论： Matt J 2021-4-23
Is there a version of the det function in R2020a that alway gives determinant 0 for small singular integer matrices?
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Rudolf Fruehwirth
Rudolf Fruehwirth 2021-4-23
And it should work without prior knowledge whether the entries are integer or not. Probably asking too much...
Matt J
Matt J 2021-4-23
And it should work without prior knowledge whether the entries are integer or not. Probably asking too much...
No, one of hte answers below meets that requirement.

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回答（2 个）

Matt J
Matt J 2021-4-23
编辑：Matt J 2021-4-23
Since you know A is an integer matrix, can't you just do,
d=round(det(A));
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Matt J
Matt J 2021-4-23
OK. Well, maybe the A(i,j) are supposed to be "small" in mangitude as well...
John D'Errico
John D'Errico 2021-4-23
Ran in:
A = randi(3,29,30);
A(end+1,:) = round(rand(1,29)*2-1)*A
A = 30×30
2 3 2 3 2 1 1 2 2 2 1 1 1 3 3 2 3 2 1 3 3 1 2 2 1 1 1 3 3 2 1 3 3 2 2 3 1 1 2 1 1 2 3 3 2 2 2 2 2 1 1 1 2 2 2 2 1 1 1 1 1 2 3 1 1 1 3 3 1 1 1 2 2 1 1 3 2 3 2 1 3 3 2 1 1 2 3 1 2 3 3 1 2 1 2 3 3 1 1 1 1 1 1 1 1 2 2 2 1 2 3 3 1 2 2 1 2 3 1 2 3 2 2 1 1 1 3 1 2 1 2 1 2 1 2 2 1 3 2 3 1 3 3 3 3 2 2 3 3 1 1 3 1 3 1 3 1 1 1 2 2 2 2 1 1 3 1 2 2 3 3 1 2 2 1 1 1 1 1 3 3 1 1 3 3 3 3 1 1 1 1 3 1 3 1 1 3 2 1 3 1 3 2 3 2 1 2 1 3 3 3 2 3 3 3 1 3 1 1 1 3 2 3 2 3 3 3 1 3 1 3 2 2 1 3 3 1 3 2 3 2 3 3 3 3 1 2 2 1 3 1 2 3 3 2 1 1 1 3 1 2 3 3 3 3 1 3 3 2 1 3 2 1 2 2 3 1 1 3 2 3 1 2 3 3 1 3 1 1 3 1 2 1 2 3 2 2 3 1 2
rank(A)
ans = 29
det(A)
ans = 0.5894
round(det(A))
ans = 1
Ok, I guess it works, some of the time. But not this one.
If the matrix is truly tiny, well yes.
A = magic(4)
A = 4×4
16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1
rank(A)
ans = 3
det(A)
ans = 5.1337e-13
round(det(A))
ans = 0
But you really cannot trust that rounding the determinant will work unless things are truly tiny.

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Matt J
Matt J 2021-4-23
编辑：Matt J 2021-4-23
Ran in:
This might work,
A = randi(10000,[9,10]);
A(end+1,:) = randi(10,[1,9])*A;
determinant=double(det(sym(A)))
determinant = 0

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