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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?
 one year ago
 one year 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?
 one year ago
 one year ago

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mykoBest ResponseYou've already chosen the best response.1
4 vectors can't form a base in 5dim space. You need at least 5 vectors
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.0
Of 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.
 one year ago

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

TomLikesPhysicsBest ResponseYou've already chosen the best response.0
Oh, 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!
 one year ago

mykoBest ResponseYou've already chosen the best response.1
you can do it in any dimention. The only thing you need is the matrix to be square
 one year ago
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