# OK mathematicians, how do I do this? **URL:** \ **Category:** Factual Questions\ **Created:** [June 3, 2006, 3:11pm UTC](https://boards.straightdope.com/t/ok-mathematicians-how-do-i-do-this/359289 "2006-06-03T15:11:22Z")\ **Posts on this page:** 9\ **Page:** 2
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [June 4, 2006, 8:55am UTC](https://boards.straightdope.com/t/ok-mathematicians-how-do-i-do-this/359289/21 "2006-06-04T08:55:04Z")
that third term in h should be h3 and not he. ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [June 4, 2006, 9:03am UTC](https://boards.straightdope.com/t/ok-mathematicians-how-do-i-do-this/359289/22 "2006-06-04T09:03:55Z")
> [@David Simmons](#): > > Oh my God, it’s unbelievably simple. > (snip) > in that case all we need do is multply both sides of h = theta\*V[sup]-1[/sup]a by a[sup]T[/sup] > > a[sup]T[/sup]h = theta\*a[sup]T[/sup]V[sup]-1[/sup]h > > which is > > 1 = theta\*a[sup]T[/sup]V[sup]-1[/sup]h Great balls of fire. It’s too early in the morning — these equations a[sup]T[/sup]h = theta\*a[sup]T[/sup]V[sup]-1[/sup]h and 1 = theta\*a[sup]T[/sup]V[sup]-1[/sup]h should be a[sup]T[/sup]h = theta\*a[sup]T[/sup]V[sup]-1[/sup] **a** and 1 = theta\*a[sup]T[/sup]V[sup]-1[/sup] **a** ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 4, 2006, 2:01pm UTC](https://boards.straightdope.com/t/ok-mathematicians-how-do-i-do-this/359289/23 "2006-06-04T14:01:53Z")
> [@Mathochist](#): > > Btw, **ultrafilter** while such forms _can_ be diagonalized, I don’t think most books assume that from the get-go. I’m not clear on what this means. Can you elaborate? ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 4, 2006, 5:45pm UTC](https://boards.straightdope.com/t/ok-mathematicians-how-do-i-do-this/359289/24 "2006-06-04T17:45:04Z")
> [@ultrafilter](#): > > I’m not clear on what this means. Can you elaborate? I’m actually beginning to think that S[sub]i[/sub] was your notation for “sum over i”. I’d originally parsed it as a diagonal matrix of coefficients. The rest of the post assumes that’s what you meant (which may well be false) In general, an inner product is a symmetric bilinear form, which can be given in matrices by **u** · **v** = **u** [sup]T[/sup]S **v** = \Sigma[sub]i,j=1[/sub][sup]n[/sup] **u** [sub]i[/sub]S[sub]ij[/sub] **v** [sub]j[/sub] Where S is a symmetric n-by-n matrix. In general over the real numbers (and many other situations) we can choose a basis so that the matrix S is diagonal, which could be written (suppressing the summation sign) S[sub]i[/sub] **u** [sub]i[/sub] **v** [sub]i[/sub] ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 4, 2006, 6:03pm UTC](https://boards.straightdope.com/t/ok-mathematicians-how-do-i-do-this/359289/25 "2006-06-04T18:03:17Z")
> [@Mathochist](#): > > I’m actually beginning to think that S[sub]i[/sub] was your notation for “sum over i”. Yes, that is what I meant. I was hoping the bounds would be clear from context. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [June 4, 2006, 6:11pm UTC](https://boards.straightdope.com/t/ok-mathematicians-how-do-i-do-this/359289/26 "2006-06-04T18:11:35Z")
> [@ultrafilter](#): > > Yes, that is what I meant. I was hoping the bounds would be clear from context. What we _need_ is a bulletin-board that recognizes LaTeX. ---
**Author:** ![Measure\_for\_Measure](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/measure_for_measure/32/557_2.png) [@Measure\_for\_Measure](https://boards.straightdope.com/u/Measure_for_Measure)\ **Post date:** [June 4, 2006, 6:22pm UTC](https://boards.straightdope.com/t/ok-mathematicians-how-do-i-do-this/359289/27 "2006-06-04T18:22:31Z")
Thanks **David** : you nailed it. a’h = h’a : Yikes, why didn’t I see that? ---
**Author:** ![Measure\_for\_Measure](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/measure_for_measure/32/557_2.png) [@Measure\_for\_Measure](https://boards.straightdope.com/u/Measure_for_Measure)\ **Post date:** [June 4, 2006, 6:23pm UTC](https://boards.straightdope.com/t/ok-mathematicians-how-do-i-do-this/359289/28 "2006-06-04T18:23:41Z")
> [@Mathochist](#): > > What we _need_ is a bulletin-board that recognizes LaTeX. …and permits inserted images (a graph every now and then can be diverting). ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [June 4, 2006, 7:59pm UTC](https://boards.straightdope.com/t/ok-mathematicians-how-do-i-do-this/359289/29 "2006-06-04T19:59:56Z")
> [@Measure for Measure](#): > > Thanks **David** : you nailed it. > > a’h = h’a : Yikes, why didn’t I see that? You didn’t see it? Who did? We don’t do these things every day. If we did we would immediately see that h[sup]T[/sup]a is the dot product h·a and the dot product is commutative so it’s equal to a·h or a[sup]T[/sup]h. [Previous page](https://boards.straightdope.com/t/ok-mathematicians-how-do-i-do-this/359289.md?page=1)