The textbook describes pseudovector like this: Let $a,b$ be vectors and $c=a\times b$, $P$ be the parity operator. Then $P(a)=-a,P(b)=-b$ by definition. But $P(c)=c$ since both $a$ and $b$ reverse ...
A tensor of type (r,s) on a vector space V is a C-valued function T on V×V×...×V×W×W×...×W (there are r V's and s W's in which W is dual space of V) which is linear in each argument. We take (0, 0) ...
I must tell you that I have never seen this kind of question in Tensor Analysis. Our professor had set up this question in our exam, but I don't know whether it belongs to tensors or not. The question ...
I studied contravariance and covariance concepts in following way: For any vector if we get its components by parallelogram way we achieve contravariant components, and if we want to get its ...
I read somewhere people write gradient in covariant form because of their proposes. I think gradient expanded in covariant basis $i$, $j$, $k$, so by invariance nature of vectors, component of ...
A vector space is a set whose elements satisfy certain axioms. Now there are physical entities that satisfy these properties, which may not be arrows. A co-ordinate transformation is linear map from a ...
I would like to know what are the range of validity of the following statement: Covariant vectors are representable as row vectors. Contravariant vectors are representable as column vectors. ...