On Thu, Nov 20, 2025 at 07:02:53PM -0800, Alan Grayson wrote: > > > I studied linear algebra, but my questions involve tensors. If a tensor > T is defined as a linear function whose domain is a vector space, and > maps to a real number, how does one get a real number from T(u), if we > do the calculation using matrices? Here there is no v, just u. AG
A matrix corresponds to a rank 2 tensor, ie T(u,v)∈R. T(u)∈R corresponds to a rank 1 tensor. In matrix notation, a rank 1 tensor is a transposed vector, ie vᵀ for some vector v∈Rⁿ. vᵀu in matrix notation corresponds to v.u (ie dot or inner product of two vectors). -- ---------------------------------------------------------------------------- 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/aSDnOoGj9G6yAW9-%40zen.
