If two vectors like in the image having angel not 90 degree between each other, can we still say they are linear indepentent? I seem to remember we only say two vectors are linear indepentent if they are perpendicular to each other.
Hi @flyunicorn ,
Two vectors can be linear independent even they are not perpendicular, because it is not just the angle, but the direction that determines independence.
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Is linear independence covered in the lectures?
A set of vectors is linearly independent if no vector in the set can be expressed as a linear combination of the others. Essentially, for the case of 2 vectors, this means the following does not stand unless a_1 = a_2 = 0:
Therefore, for 2 vectors to be linearly dependent, they must be parallel. If they are not parallel, they are linearly independent.
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I wonder if I got it confused of the eigenvector in PCA where the two eigenvector needs to be perpendicular to each other. But outside PCA, it seems eigenvector doesn’t need to be perpendicular to each other. Is this correct?
No, eigenvectors are not always perpendicular to each other. You may quickly test some examples online.
There is a special case that for a certain kind of matrix, its eigenvectors are orthogonal, but I will leave it to you to google that out 
Cheers,
Raymond