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Apr
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Dec
24
accepted covariant and contravariant components and change of basis
Dec
23
comment Can the gradient be expressed with contravariant components?
Isn't $V^*$ isomorphic to $V$ for $\mathbb{R}^n$? And if $V^*$ should be kept separate from $V$ then what does "every vector has both contravariant and covariant components that transform in predictable ways" mean if the gradient can't be expressed in basis vectors in $V$ and must be expressed in components with basis vectors in $V^*$.
Dec
23
comment Components of vector in dual basis transform covariantly
I don't understand the significance of saying they "live in the dual space".
Dec
23
comment Can the gradient be expressed with contravariant components?
Covariant basis vectors are the same as dual basis are they not?
Dec
23
comment Components of vector in dual basis transform covariantly
Covariant basis vectors are the same as dual basis are they not?
Dec
22
asked Can the gradient be expressed with contravariant components?
Dec
22
asked Components of vector in dual basis transform covariantly
Dec
22
awarded  Caucus
Dec
18
revised covariant and contravariant components and change of basis
added 104 characters in body
Dec
18
comment covariant and contravariant components and change of basis
In the book it shows the direct transformation matrix on the left hand side whereas here you have it on the right side. That is what is confusing me.
Dec
18
revised covariant and contravariant components and change of basis
edited title