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Can somebody explain me the name and/or intuition behind this equation?

dm(A,B)=max{∥(A−B)x∥:x∈Rn,∥x∥=1}

Kindly refer the equation here: Distance/Similarity between two matrices

EDIT: I posted it here as I didn't have enough reputation to comment and ask in the above question link. Thus, kindly vote the question if possible.

Rushabh Mehta
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Ravi
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  • Just a guess from reading the equation but:

    If $||x||=1$ then it is a unit (therefore somehow standardised) vector. Matrix $A$ applied to such a vector would transform it somehow. So will matrix $B$. The measure is a difference of that transformation. If the difference in the resulting vectors is big, then you might say that $A$ and $B$ are producing quite a different result and the "difference" between the matrices is big. If you try all of the $x$ values to see which causes the biggest (max) change, then you are just using that largest seen change as a way of comparing all vectors.

     – Benedict W. J. Irwin Nov 14 '19 at 16:59
  • @BenedictW.J.Irwin , I was thinking ||x||=1 as an hypersphere in the n-D space and x as all the points on the sphere. Is it a wrong assumption? and any names for this equation? – Ravi Nov 14 '19 at 17:21
  • And regarding that transform, let's say we have another matrix C which is dissimilr w.r.t. B, can the transforms from A-B and A-C have almost same transformation effect on the unit vector x? – Ravi Nov 14 '19 at 17:28
  • As in, Can A-B and A-C may result in some kind of rotational transformation(say 1 degree and 361 degree respectively) causing the results of dm(A,B) and dm(A,C) to be similar? – Ravi Nov 14 '19 at 17:54
  • FYI, if you go over to that other thread, there are two ways you can see how to format the expression you copied. (1) Right-click on the formula. You will see the option "Show Math As" > "TeX Commands". Select that and it opens a textbox with the mathjax formatting. Copy this to your on post, and put $$ at the front and back of it, and you will get exactly what you see there. If you put only one $ at each end, you will get the in-line version. (2) Click on the "edited Sep 30 '13 at 7:28" link on the bottom. You can see the edit history. Click on Markdown and you can see the formatting. – Paul Sinclair Nov 15 '19 at 01:40

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