Need help with subspace basis

2019 12 1
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更新时间：2019 12 12
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I'm writing a script to find the basis of subspace spanned by a vector set and by a homogenous system. In the case with the vector set, I plan to put my given matrix through rref to find the pivots and from there point out the vectors that are the bases.
Here's what I got so far
disp('input matrix')
A = input('A=')
Ar = rref(A)
s = size(Ar)
s1=s(1)
s2=s(2)
for i=1:s1
for i=1:s2
if Ar(i)== 1
A(:,i)
end
end
end

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KALYAN ACHARJYA
KALYAN ACHARJYA 2019-12-1
for i=1:s1
for i=1:s2
end
Is both are "i"?
Jacked Daniel
Jacked Daniel 2019-12-1
yeah but they I don't think it matters, I changed it to t and had the same results. I also used two i(s) before for two different for loops and it was fine then.

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回答（1 个）

Matt J
Matt J 2019-12-1

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You could just use orth()

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Jacked Daniel
Jacked Daniel 2019-12-3
I read the description of the orth command, at first it seemed like the "Easy button" for me but the values it returns are not what I expected. I still can't fully understand how the orth command works and the basis it returns is completely different from what I get solving by hand.
Matt J
Matt J 2019-12-3
You do realize that the basis for any linear space is non-unique, right?
Jacked Daniel
Jacked Daniel 2019-12-12
Yes and are you suggesting that the ugly combination of entries I received is a basis? I do agree but I can't show that to my teacher cause she's gonna check and compare my MATLAB basis to her do-it-by-hand basis. So I can't use the orth command BUT the null command I use for the case of subspace spanned by homogenous systems is quite handy. It returns the exact value I expect it would. Oh and I figured out how to work the code, I added a "break" command and it is looking good. Thanks for helping me.

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