Difference between revisions of "Manuals/calci/QUATERNION"

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*<math>i\sdot j </math> =<math>k</math> = <math> -j \sdot i </math>  
 
*<math>i\sdot j </math> =<math>k</math> = <math> -j \sdot i </math>  
 
*<math>j\sdot k </math> =<math>i</math> =<math>  -k\sdot j </math>  
 
*<math>j\sdot k </math> =<math>i</math> =<math>  -k\sdot j </math>  
**<math>k\sdot i </math> =<math>j</math> = <math> -i\sdot k </math>
+
*<math>k\sdot i </math> =<math>j</math> = <math> -i\sdot k </math>
 
 
 
 
 
 
*<math>i\sdot j </math> =<math>k</math>= <math> −j \sdot i</math>,<math>j\sdot k </math>= <math>i</math> = <math>−k\sdot j</math>, <math>k \sdot i</math> = <math>j</math> = <math> −i \sdotk</math>
 
  
 
==Examples==
 
==Examples==

Revision as of 14:45, 17 January 2018

QUATERNION (a,b,c,d)


  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a,b,c} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d} are any real numbers.

Description

  • This function shows the coefficient of the Quarternion.
  • In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle QUATERNION (a,b,c,d)} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a,b,c } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d} are any real numbers.
  • Quartenion is a complex number of the form w + xi + yj + zk, where w, x, y, z are real numbers and i, j, k are imaginary units.
  • The imaginary units are satisfy certain conditions:
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i^{2}=j^2=k^2=ijk= -1} .
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i\sdot j } =Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -j \sdot i }
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j\sdot k } =Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i} =Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -k\sdot j }
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k\sdot i } =Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -i\sdot k }

Examples

  1. QUATERNION(9,2,3,4) = 9 2 3 4
  2. QUATERNION(8,-2,4,-5) = 8 -2 4 -5
  3. QUATERNION(-9,-12,-16,-20) = -9 -12 -16 -20

See Also

References

Quartenion