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TomLikesPhysics
 2 years ago
I have 4 different vectors with 5 components. What is the fastest way to determine if these vectors form a linearly independent base in 5dim space?
TomLikesPhysics
 2 years ago
I have 4 different vectors with 5 components. What is the fastest way to determine if these vectors form a linearly independent base in 5dim space?

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myko
 2 years ago
Best ResponseYou've already chosen the best response.14 vectors can't form a base in 5dim space. You need at least 5 vectors

TomLikesPhysics
 2 years ago
Best ResponseYou've already chosen the best response.0Of course... Well, how do I check if 5 vectors with 5 components form a linearly independet base? Let´s say it is not obvious and there is not a vector who looks like a multiple of another vector.

myko
 2 years ago
Best ResponseYou've already chosen the best response.1check determinant of matrix formed by this vectors. If it's equals 0 vectors are dependent. If not  independent.

TomLikesPhysics
 2 years ago
Best ResponseYou've already chosen the best response.0Oh, I did not know that I can use a determinant with vectors which are in a higher dim. than 3. Thx for your help myko!

myko
 2 years ago
Best ResponseYou've already chosen the best response.1you can do it in any dimention. The only thing you need is the matrix to be square
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