On Thu, Nov 20, 2025 at 01:07:19AM -0800, Alan Grayson wrote: > > > On Thursday, November 20, 2025 at 2:02:07 AM UTC-7 Russell Standish wrote: > > On Tue, Nov 18, 2025 at 11:31:22PM -0800, Alan Grayson wrote: > > > > > > On Monday, November 17, 2025 at 9:54:00 PM UTC-7 Russell Standish wrote: > > This is Linear Algebra 101. > > > > To convince yourself, try it with a 2x2 matrix to make the > > calculations easier. Extending the result to Rⁿis not difficult. > > > > Exercise: > > > > Show that > > > > (auᵀ₁+buᵀ₂)Mv = auᵀ₁Mv + buᵀ₂Mv > > > > and > > > > uᵀM(av₁+bv₂)=auᵀMv₁+ buᵀMv₂ > > > > for a,b∈R, uᵢ,vᵢ ∈ Rⁿ, and M a real valued matrix. > > > > The above two lines are the definition of a bilinear function from Rⁿ⟶ > R. > > > > > > If they're definitions, there's nothing to be shown or proven. But I > have > two > > questions relating to this subject. First, since uᵀ is a column matrix, > is it > > OK > > to place it on the RHS of M, with the convention that Muᵀ is evaluated > first, > > followed by the result being evaluated by applying v (a row matrix), so > we > > we get a real constant as the result? Second, if the function has one > > independent variable, say u, I don't see how we can use matrix notation > to > > evaluate the tensor To get a real value as the result. TY, AG > > You mean uᵀv=u.v∈R? In this case u is a vector, and uᵀ is a rank 1 tensor. > > Cheers > > > Forget it. I see you're not really interested in answering my question. AG
I'm trying to guess what your question means, and then to answer it, Maybe try rephrasing it. I'm not trying to diss you, but this stuff really is Linear Algebra 101. I don't know if you ever studied that in the past, and forgotten stuff, or got a confusing presentation on matrix calculations that creates more confusion than enlightenment (a lot of mathematics courses for engineers is like that, sadly), or that you completely missed studying that. In any case, it might be worthwhile you going through some of the Wikipedia pages on the subject - generally Wikipedia does a fairly good job on mathematical topics, though I can't specifically recommend their treatment of Linear Algebra. In fact my Linear Algebra lecturer specifically thought all textbooks on the subject were bunk, admittedly this was 4 decades ago, so things might have improved. > > > -- > > > ---------------------------------------------------------------------------- > > 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 > /49f41010-2de8-469a-9769-fbff590a4cafn%40googlegroups.com. -- ---------------------------------------------------------------------------- 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/aR-43rxicdfncH-M%40zen.
