Quaternions and the ather hypercomplexe numbers

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SUMMARY

Quaternions and other hypercomplex numbers, such as octonions and sedenions, provide solutions to equations like x² + 1 = 0, demonstrating their mathematical significance. They are integral in various physics applications, particularly in areas involving rotations and complex transformations. John Baez's website serves as a valuable resource for understanding the role of these numbers in physics.

PREREQUISITES
  • Understanding of quaternion algebra
  • Familiarity with hypercomplex numbers
  • Basic knowledge of complex analysis
  • Awareness of mathematical physics concepts
NEXT STEPS
  • Explore quaternion algebra and its applications in 3D rotations
  • Research octonions and their properties in higher-dimensional spaces
  • Investigate sedenions and their role in theoretical physics
  • Visit John Baez's website for insights on hypercomplex numbers in physics
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Mathematicians, physicists, and students interested in advanced algebraic structures and their applications in theoretical physics.

matteo16
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apologie me if this question isn't corret or is simple for you

do solutions of an equation as quaternions or as the ather hypercomplex numbers exist?

wath do they do in physics?

for exemple ottonions or sedenions

do ather hypercomplex numbers exist?
 
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Yes, of course there are solutions in quaternions to things like x^2+1=0 (there are many, in fact, that being the whole point) and of course the real numbers are a subset of the quaternions...

As for physics, look at John Baez's website (google for it).
 

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