For some context, I am learning about the cross product, and the matrix we used as an example was: bbV=[[vec(v)_1],[vec(v)_2],[vec(v)_3]] which I am told is a 3 xx 3 matrix. But since these vectors are in 3 dimensions, wouldn't they also be column vectors? How do we get to a 3 xx 3 square from that?

furajat4h 2022-09-22 Answered
For some context, I am learning about the cross product, and the matrix we used as an example was: V = [ v 1 v 2 v 3 ] which I am told is a 3 × 3 matrix. But since these vectors are in 3 dimensions, wouldn't they also be column vectors? How do we get to a 3 × 3 square from that?
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Answers (1)

efterynzl
Answered 2022-09-23 Author has 12 answers
Don't worry, it's just a matter of notation : if v i = ( v i 1 , v i 2 , v i 3 ) (where I write v i to indicate the i-th vector and v j the component, following you notation -I eliminate the arrow to simplify it-), the matrix V you obtain is
( v 1 1 v 1 2 v 1 3 v 2 1 v 2 2 v 2 3 v 3 1 v 3 2 v 3 3 )
Otherwise you consider V T = [ v 1 , v 2 , v 3 ], and then you list your vectors in column. Hope it help!
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