Re: Wald's Isomorphism between V and V*

[Mike_Fontenot]

I already spotted one typo, and one omission, in my previous post:

First, the typo. I wrote:

(quote)
"I also like to be able to make explicit the difference between a MAP
itself, versus the target of a map (a number). I do that by adding a
subscript to a post-index, when I intend that post-index to represent a
specific value for the argument. (And I also use the same idea for
pre-indices). For example,

V{sup a}

is a MAP from duals to numbers, whereas

V{sup a0}

is a number, produced when the argument to V is the specific dual {sub
a0}W. I.e.,

V( {sub a0}W ) = V{sup a0}.

(When I handwrite the above, I write the "0" as a subscript on the
"a"...but that's too confusing to do in ASCII)."
(end quote)

I SHOULD have written:

(start correction)
V{sup a0}

is a number, produced when the argument to V is the specific dual {sup
a0}W. I.e.,

V( {sup a0}W ) = V{sup a0}.
(end correction)

I also intended to give an example to make clear how the optional
pre-index of tensors of order greater than one are used. For example,
to add a pre-index to the example (2,3) tensor T given in the previous
post, you can write

{sub f}T{sup ab}{sub cde},

where the added pre-index "f" is a subscript, because the first argument
"a" is a dual, and a dual will be the argument to a basis VECTOR
whenever T is written as a weighted sum of outer-products of two basis
vectors and three basis duals. So, the pre-index will always have the
opposite position (up vs down) to the first post-index.

Mike Fontenot