On Friday, November 28, 2025 at 3:17:02 PM UTC-7 Russell Standish wrote:
On Tue, Nov 25, 2025 at 12:48:59PM -0800, Alan Grayson wrote: > > On other thing; when evaluating the tensor T(u), how do you know which > co-vector (member of dual vector space) to use, or doesn't it matter? > Won't different co-vectors result in different real values for the tensor? AG The set of linear functions from Rⁿ→R is a vector space. The numerical values of the components of the vector depend on your chosen basis, of course, which is quite arbitrary, however it is usually convenient to choose a basis dᵢ of the dual space such that "orthoginality" relations hold woith respect you chosen basis eⱼ of the original vector space, ie: dᵢ(eⱼ) = δᵢⱼ Given any basis of a vector space, you can orthonormalise them by means of an algorithm call "Gram-Schmidt orthonormalisation". *I recall that theorem in a book I studied, Halmos, Finite Dimensional Vector* *Spaces. AG * ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/a3d86799-8462-4bd0-868f-b5694eb42c98n%40googlegroups.com.
