It’s not nessecary, it’s a form of optimization or ease of computation.

If you do not rotate the components, the inherent attributes of the metric informational points of the underlying co-ordinate system, will sustain as they are.

The fundamental part of the alignment and the “reconstruction” of the Matrises - inherently means to “adjust” a piece of the larger set of metric points.

Granted - it may become less computable or less forgiving to substansiate other follow up conditions - but it largely is a form of easing.

You can say that, some relaxations of conditions - have pre-requisites by virtue of compositional compounded follow-up rules of implicative relation stature.

I.e - “If A is TRUE, then B is TRUE” - that kind of ordeal.

But in a gradient.

So, “If A is 90% TRUE, then we could simplify B by 20%”

This is extremely, grossly oversimplifying it.

But it stands to reason to be a form of a trick, to ease computation or lessen the extent of “Enforced” methodology.

In general - when it comes to Matrises and the general predicament of Orthogonality, Orthonormal, Bases, Structural integrity and a Normed 3D space - you generally pay by virtue of indirect connotations of implicative stature -

i.e, in case of inversions or accounting for a certain set of Eigenvalues or Eigen vectors, etc.

The larger predicament and the larger problematic stature - in relation to such systems - can be constriction in terms of computational means.

You can always theoretically execute the simplification if it abides by rules.

The same, cannot be said in terms of the Physical underlying simulatory stature or the predicament of the basing of the implementation of the Language you run it in.

If you were to deviate too far from the substructuring in terms of Sub-spaces, Manifolds and Dimensional relations - be that compression, density or structural complexity - you would implicate loss of efficiency or outright error of predicament.

Issues that can arise ranges from density issues (i.e invalidation of certain algorithmics, due to nature of being “greedy” or equally so, “being lazy”).

Other issues that can arise, is violation of basing of the structural integrity and the conditions required to entail to minimize things like the Collective Entropy of the system.

It’s not nessecarily that “the solution is wrong”, it could just outright be that the degree of information of the closed system - is redued - due to less traversability of the system - in relation to node tree sub divisionaries and things akin to Matris structuring in terms of accessing things like the Eigen Values.

Consider the fundamental structural composition of the sub iterative fashion of Sigmatic Sums, and you will come to find that under the error of alignment - the entropy is increased in some cases - due to less ascertainability or violations of structuring in terms of Accessing structure of Algorithmics.

An apt comparison, would be that - you could “maximize space”, if you “stack your boxes nicely” - comparatively to jumbelling them.

That’s a very crude metaphor.

But it goes to predicate the fundamental implication of the structural adhesive nature in terms of metric point accessing.

What you really do in terms of Optimizations with Rotations and otherwise - is to try to minimize the Entropy - to maximize the equilibrium in the system - i.e, enforcing attributation in such a form that you can ascertain the most information from the system.

It alleviates costing, ascertains that the solution forming is as cohesive and sustained as can be - due to following the theoretical implicative stature of the calculations.

You can see the algorithms as the “rules to be enforced” - where the physical simulation - may need some “applied force” - to obey.

I.e - simplifications, circumventions, rotations, conversions - or other factors.

Perhaps once i am more well versed in Math, i will be able to bring out some examples of this.

It’s extremely fascinating, none the less.