bra-ket notation

https://en.wikipedia.org/wiki/Tensor_product
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As Wayne puts it, "just enough math to be dangerous". Please be checking along.

Next seeing Hermitian (or Non-Hermitian) to mean conjugated/adjoint (or disjoint) systems. Two connected dual-pair opposed kites are Hermitian, but separated kites are not (as such).

Kite flight is Hermitian conjugated.

Hermitian adjoint
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Note: As Haldane states, entanglement is the essence of QM, which started with quantization before getting "spooky." So we are seeing all these dual-pair representations matching dual-pair kite dynamics.

Fresh from the oven (4 days ago), a paper confirming the kite-pair has caught up to the frontier of physics-

"Despite its importance, the dual pair correspondence, as we will simply refer to it, is not among the most familiar mathematical concepts in the theoretical physics community, and particularly not in those of ﬁeld and string theory, where it nevertheless appears quite often, either implicitly, or as an outcome of the analyses. For this reason, many times when the dual pair correspondence makes its occurrence in the physics literature, its role often goes unnoticed or is not being emphasized, albeit it is actually acting as an underlying governing principle."
High Energy Physics - Theory
[Submitted on 12 Jun 2020]
Dual Pair Correspondence in Physics: Oscillator Realizations and Representations
Thomas Basile, Euihun Joung, Karapet Mkrtchyan, Matin Mojaza

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June 16, 2020, post by Joe Faust
Dave,
1. Since my math beginnings, I kept a lateral poetic license to form a meditative and prayerful space evolving that springboarded from the mathematics being studied. The poetic expressions were not mathematics. E.g.: trig: sin 90 degrees is 1 [transgressions or sin upon crossing or perpendicularity is oneness]

2. My relative silence over your excited movements regarding QM, tensors, kite matter, etc. is not to be taken as understanding nor agreement that the excursions form a sound system of thought. I am ever playing catch-up on these matters. My course in vector analysis was challenging; I did not master what is known. I completed 90% of the pure mathematics master's degree program with top grades; I completed with honors the B.A. in pure mathematics. I taught several college math classes. My master's degree program thesis project was robustly made over the circle. I chose not to complete the program and chose also not to complete the 90%-completed teaching credential program. I believe in creative poetic math-realm adventures, but have confidence that scientifically effective novel findings are not easy to form. The story of Georg Cantor could be a warning here regarding transcendental numbers; he did have some important matter but may have become sick because of the peer resistance of his findings. I say: Go for it (the adventure), for without the adventure there will be no novel breakthroughs. But within a set of certain assumptions where 2+2=4, it can be shown that there are uncountable many wrong answers for 2+2=? when the assumptions are kept in force. Yet, one is free in poetry (setting aside some assumptions) to play with, say: 2+2=22 or, say, 2+2=giraffe.
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June 16, 2020, post by Dave Santos
Given infinite numbers, its a remarkable coincidence if 2+2 always equals 4. Poor Cantor, from Jew to Lutheran, then his transfinite numbers taken as proving paganism. Anyone would go mad after that. Even sadder, he could have been helped with kite therapy (stoke). Wittgenstein was saved by chance, as a kite researcher.

I'm only asking for school teacher correctness of usage. For I long time (non)Hermitian seemed to me like a closed v. open thermodynamic system, guessing by the name, but that was wrong now that I look it up, and now I can use it. Our job is different than Cantor's, in matching the crazy kite to any applicable math that suggests possibilities. We are coming from kite madness to math, as if coming from infinity to 4.

That's the strangest thing about kites, how they teach things unsuspected. When first kites are seen to fly, its infinitely astounding, the rest is transfinite, and Cantor is on the other side, depressed.