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Quaternions

Created by quaternions. Last Edited by summer. Tagged as: Ideas
Quaternions
Quaternions Quaternions

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In mathematics, quaternions are a non-commutative extension of complex (imaginary) numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. At first, quaternions were regarded as pathological, because they disobeyed the commutative law ab = ba. Although they have been superseded in most applications by vectors, they still find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations, such as in 3D computer graphics.

In modern language, quaternions form a 4-dimensional normed division algebra over real numbers. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by \mathbb H (Unicode ā„). It can also be given the Clifford algebra classifications Cā„“0,2® = Cā„“03,0®. The algebra H holds a special place in analysis since, according to the Frobenius theorem, it is one of only three finite-dimensional division rings containing the real numbers as a subring.

..and besides all this stuff, he is a great guy :)

 

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Sgt Pepper Finrod summer quaternions Marisa

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Katie
Katie posted about 1 year ago

Dude, you can’t just make up a category for yourself!

Marisa
Marisa posted about 1 year ago

He didn’t! Quaternions the person voted for quatrenions the word and quaternions the mathematics while I, Marisa the person voted for Quaternions the person as the best veteran. Because he has been here since almost the dawn of this site and has racked up some fantastic stuff on the way.

summer
summer posted about 1 year ago

Oh my dearyou are! :)

summer
summer posted about 1 year ago

edit : Oh my dear you are! :) :)

summer
summer posted about 1 year ago

LOL

I did it. I did it.

quaternions
quaternions posted about 1 year ago

I take it you were the one who was ‘curious’ about me…lol.

summer
summer posted about 1 year ago

LOL Oh yeah that was me. But I was curious about the mathematical thing actually :)

quaternions
quaternions posted about 1 year ago

Quaternions are “imaginary numbers” ;-) LOL

Finrod
Finrod posted about 1 year ago

i squared = j squared = k squared = ijk = -1. Fascinating.

I like the idea that three dyads can separately equal a triad. If I’ve got the notation terms right…

quaternions
quaternions posted about 1 year ago

Thanks for description edit summer :)

summer
summer posted about 1 year ago

Oh, not at all. That’s the truth :)

quaternions
quaternions posted about 1 year ago

Ty hon. You’re great too! How’s things? :D

summer
summer posted about 1 year ago

Fine so fine. I’m on holiday, I passed with great results, so how wouldn’t I be fine? :D I hope you’re good, too :)

quaternions
quaternions posted about 1 year ago

I knew you’d do well in the exams :) What are you doing next? A Phd?

My life is fine :)

summer
summer posted about 1 year ago

Yeah, I am closer to phd now but I still got a semester to get my masters degree.

quaternions
quaternions posted about 1 year ago

Another semester…drat :) Gotta go. Hugs xxxxx