Linearity in binary: two vectors x=(0,0,1,0) and y=(1,1,0,1)

bingnas

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HI All

I have two vectors x=(0,0,1,0) and y=(1,1,0,1), if you multiply them you got zero which mean are orthogonal (linearity independent). Someone told me that's not true, and they have perfect linear relationship y=1-x.

what the right answer please?

Thank you in advance

EM
 
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The right answer to what question? Yes, if two vectors have 0 dot product then they are "orthogonal" so "linearly independent". (The other way is not true- two vectors can be "linearly independent" even if they are not "orthogonal".)

But that has nothing to do with one being 1 minus the other. "Linearity", in the "Linear Algebra" sense requires that one vector be a multiple of the other. That is not the same as a "linear equation" connecting the two. If two vectors are "linearly dependent" then their span is a line passing through the origin. Here, their span is a line but not passing through the origin.
 
The right answer to what question? Yes, if two vectors have 0 dot product then they are "orthogonal" so "linearly independent". (The other way is not true- two vectors can be "linearly independent" even if they are not "orthogonal".)

But that has nothing to do with one being 1 minus the other. "Linearity", in the "Linear Algebra" sense requires that one vector be a multiple of the other. That is not the same as a "linear equation" connecting the two. If two vectors are "linearly dependent" then their span is a line passing through the origin. Here, their span is a line but not passing through the origin.


Thank you so much :D
 
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