Recent content by Aleberto69

Apologize Perok but your explanation is not convincing me... 1) If I have an abctract space how can I verify that ei dot ej = dij? In my opinion is a similar problem of verifying that the three vectors are left handed.. I could say if e1 x e2 = e3 (and ciclically) then the base is right...

Honestly I reply here to PeroK too. Honestly I do not have an answer to the question How the observer knows the handenss of the coordinate system that he is adopting.. However the following: 1) I can reference many Authors and text that says " the determinant rule applies only to rigth...

" ..So if you apply the same cross-product-definition to both ".... do you understand the determinant rule? what I'm saying is ( only appling to the case of passive trasformation) that the second observer knows that his base vector is left handed and therefore he should be aware that the...

right-hand rule and determinant rule are not the same thing in my opinion.. determinant rule give the same result of right ahand rule only for orthonormal rigth hand base vector.

TY weirdoguy.... you are probably rigth... and probably also other people in this thread menitoned bivectors which probaly more easily clarify the point.. I 'll get an insight to this more sophisicated tools later on soon. However, restricting the matematics to the simple vector algebra.. do...

Hi PeroK, I have no doubts about the rules for the cross product and theri differences. Let consider a cartesian orthonormal system of cordinates and its natural base vector i', j' and k' ( natural meaning that the unit vector of the base point to the same direction towards the relative...

Hi A.T. thank you for your reply.. I agree with you that in your example "Here, when you mirror �→, then �→ is not just mirrored, but mirrored and negated. So �→ and �→ behave differently under a mirror transformation." However I want to ask you a question about that example : are the the two...

Hi PeroK again ..I read posts on the link you gave me again... I spotted two interesting things that come to my side.. one is on the second to last post.. It treats the matter with tensor using the levi-cita one. I started studing tensor and I understnd them a bit.. What I noticed is that they...

Hi PeroK Thank you for the reply. I read the link and in the first replying posts it is a bit more complex than simple linear algebra. I ' have not the knoledge to completely get that comment.. I do not kow what you want to enphasize about the link, however the last post of it talk about left...

I thank you for your kindness... why don 't we discuss in italian .. can you? anyway ....did you read my attempt to explain my doubts in my last post to you? have you some comments on that insted of being hilarious?.. is there something that I didn't explain well ? or that I didn't calculate...

agree!! but it is commonly accepted that if the base vector is RHanded i x j = k. That is not a definition of k but somethig that is commonly accepted to be true.. any cross product can be reduced to a sum of pieces .. all of them including a pair of vector from the base (and a...

Hi A.T. apologize for not completely understend... what do you mean for the right leg and left leg? could you traslate the example using coordinate trasformations...? I try to start with it.. I have a force and a lever arm ... let F is a vector its components are (0,1,0) ( tey are...

ok.. x y z are coordinates or components? in cartesian system it is easy to confuse the two concepts.. However let assume you confirm "components", this means that your trasformation of coordinate implies also this trasformation of components of a vector.. I would also add that it implies...

About the ijk coomment.. A: I know that k is not special... I could have pointed on j x k= i as well.... then I do not understand what is the difficulty with handness of the base.... when with start with vectors.. and base vectors ... nobody care of saying nothing about handness... the...

Hi PeroK, I have an issue with your text .. I do not se properly the latex formulas ( eg I see ##c' \ne a' \times b'## ??????). However I do not uderstand even at your beginning when you say "...we do a transformation such that every vector is mapped to the negative" ... I do not...