
#1
Jan613, 08:43 PM

P: 375

A= i +j+k
A=(1,1,1) can I write in vertical as shown? is there any difference between them? Thank you 



#2
Jan713, 06:15 AM

Sci Advisor
HW Helper
Thanks
P: 26,167

Hi Outrageous!
(i'm puzzled as to why you said "complex" … you're not thinking of quaternions, are you? ) one is covariant, the other is contravariant (i can never remember which is which ) for most purposes, it doesn't matter, so you might as well write everything horizontally, since that's more convenient! 



#3
Jan713, 06:47 AM

P: 375

Thank you. That should be vector.
How to edit title? 



#4
Jan713, 07:08 AM

Sci Advisor
HW Helper
Thanks
P: 26,167

Vectors  write ordered triples in vertical or horizontal form?
i don't think can edit the title
(but you can edit the first post, to say "ignore the title!!" ) 



#5
Jan713, 09:42 AM

Mentor
P: 21,018

Title changed




#6
Jan713, 01:18 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,885

This is a bit more abstract and advanced but one way of looking at it is this: Given an ndimensional vector space, V, over field F, the set of all functions from V to F, the "dual space" to V, is itself a vector space, V*, with addition defined by (f+ g)(v)= f(v)+ g(v) and (af)v= a(f(v)), also of dimenion n. We can then represent functions in V* as "row matrices" and the vectors in V as "column matrices" so that the operation f(v) is a matrix multipication.
However, because it is still true that V and V*, both being ndimensional vector spaces, are isomorphic we can identify one with the other, the row and column matrices as both representing vectors and think of the matrix multiplication as an "inner product" on a vector space. 



#7
Jan713, 10:15 PM

P: 375

Really advanced. Thank you.



Register to reply 
Related Discussions  
Number of diffracted orders produced  Introductory Physics Homework  2  
write out the expression for the vertical velocity  Calculus & Beyond Homework  6  
Write an equation of each horizontal tangent line to the curve.  Calculus & Beyond Homework  3  
Orders of poles in the complex plane.  Calculus & Beyond Homework  0  
Horizontal oscillations to vertical.  Mechanical Engineering  2 