MotleyNoumenon

Lol its probably just a troll. Maybe another user pulling a bit..

how rude haha! Quando discis latinum dicere?

They are the same in the sense that both are curves, but just because you can deform a circle into a square doesn't mean that a circle has four corners, or a square is smooth. In the generality that you seem to intend it is trivially false.

Not sure i get what you want to say but it sounds like this thing which "becomes" a square is supposed to "remember" that it was a circle? similarly with the colors. If it were not for this i would agree with @Strange that it sound like the Theseus' ship problem. Let me put forward another view, that change depends on the observer.

Probably a wrong one, in the right eyes. However, in the case of giving a definition i suppose i think of space in the spacetime manifold sense. Which also shows my point: Volume is a measure of space, in the manifold sense. This is also intrinsic. As to the latter part, it should be evident that if volume is a measure of space then it is not space it self. I think i can see how you can equate them but its a bit artificial and forced imo, so i would rather hear your ''notion of space" and your arguments for why volume is a property (of what precisely? objects?), and why it equates with your notion of space. I suspect that your definition might be something along the lines of "volume is the space a thing occupies" (not to put words in your mouth! please, correct me), in which case i totally see your point of view. I think we had different initial contexts in mind, and thats why i disagreed.

Apply the definition? look at the symmetry, maybe use some known decomposition of this sort of matrix and apply properties of the determinant.. these are just thoughts..

Shouldn't this be in the Speculation section, i dont see how any of this is about math.

Not sure i should dip my toes in here but volume is a measure, not a property (although you can view it as a property, but this is nontheless extrinsic) and certainly not equatable with space.

I suppose one application is as a hint for pattern-recognition, it can give you an idea what to look for. An example could be when one considers symmetrical objects, this is daily life for some.. in this context the theorem (which is so natural that you never really think about it, you just use it) can hint at components of the object which can correspond to sub-symmetries.. so in some sense you loosely use it together with some implicit monotone galois connection. Though i dont know what a plumber would do with it unless they're pulling some Good Will Hunting bit...

Its a social construct, thus the question of whether there is any in war boils down to what the culture of the considered side is like, or both in some cases. But generally i doubt its something that manifests in all societies. On the other hand there may be analogous of glory in other cultures that are just very similiar to the western concept. Maybe you could be more specific, things are just very open ended otherwise.

Well, as stated the first part has only one solution, the zero matrix; on the other hand the zero matrix is skew-symmetric.. The first part could be modified but why bother, its gonna be a rotation of \( \pi/2 \) radians in some direction, i.e. the solution space could be visualized as a circle with every point a matrix.

Yes! Lets create a society of super beings where every market, hierarchy and competitive structure lends it self to total corruption! It would clearly solve our most important problems, the physiological ones, and not those pleasing, agreable and outright delightful psychological idiosyncracies.

I would guess that this is "sort of weakly" formalised using model theory and categories.. Just curious. However, back on topic: I agree with the others that there are definitional issues and the latter part makes no sense in the contexts that we are familiar with. Perhaps you could enlighten us on what kind of concepts you are talking about, and if they are not mathematical, i.e. defined within our framework, then i suppose this thread should really be in the philosophy section.

First I was wondering by what calculate means, but eitherway i dont think there is a closed form.

This is on the level of Hilbert space theory, which (if you have seen it) isn't that difficult to understand, but usually one learns of this from Fourier analysis. This and the more general inequality can be found in the section "Relations between p-norms" : https://www.wikiwand.com/en/Lp_space#The_p-norm_in_finite_dimensions. You can find a proof of it at https://math.stackexchange.com/questions/245052/showing-that-l-2-norm-is-smaller-than-l-1.