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## Main Question or Discussion Point

In

http://en.wikipedia.org/wiki/Covector#Bases_in_finite_dimensions

For example, Griffel writes as follows:

Let [tex]x_{r}[/tex] be the

[tex](a)\; g^{r} = g\left(e_{r} \right)[/tex]

[tex](b)\; g\left(x \right) = \sum_{}^{} g^{r} x_{r}[/tex]

If this does differ from normal usage, as I suspect, how would it be rewritten according to the usual convention? Should I put the index on

And where he writes

There is a basis [tex]\left\{f_{i},...,f_{n}\right\}[/tex] for [tex]V^{\ast}[/tex], called the dual basis, such that

[tex]f_{r}\left(e_{s} \right) = \delta_{rs}[/tex], for r,s = 1,...,n

would the normal convention be for the index written

Any advice welcome!

*Linear Algebra and its Applications*, David Griffel writes, "The components of covectors are often denoted by superscripts, rather than subscripts." This differs from the usual convention, doesn't it? Unless I've completely misunderstood the concept (quite possible!), the introductory texts that I've seen so far have denoted the components of vectors with superscripts, and the components of covectors (one-forms, linear function(al)s) with subscripts). E.g.http://en.wikipedia.org/wiki/Covector#Bases_in_finite_dimensions

For example, Griffel writes as follows:

Let [tex]x_{r}[/tex] be the

*r*th component of a vector*x*in*V*with respect to a basis [tex]\left\{e_{i},...,e_{n}\right\}[/tex], and [tex]g^{r}[/tex] the*r*th component of a covector*g*with respect to the dual basis. Then[tex](a)\; g^{r} = g\left(e_{r} \right)[/tex]

[tex](b)\; g\left(x \right) = \sum_{}^{} g^{r} x_{r}[/tex]

If this does differ from normal usage, as I suspect, how would it be rewritten according to the usual convention? Should I put the index on

*g*down, and the index on*x*up, and leave the index down on*e*?And where he writes

There is a basis [tex]\left\{f_{i},...,f_{n}\right\}[/tex] for [tex]V^{\ast}[/tex], called the dual basis, such that

[tex]f_{r}\left(e_{s} \right) = \delta_{rs}[/tex], for r,s = 1,...,n

would the normal convention be for the index written

*r*to appear as a superscript on the basis of the dual space [tex]V^{\ast}[/tex], and for the Kronecker's delta here to have superscript*r*and subscript*s*?Any advice welcome!

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