Difference between revisions of "Manuals/calci/QUATERNION"

From ZCubes Wiki
Jump to navigation Jump to search
 
(12 intermediate revisions by the same user not shown)
Line 7: Line 7:
 
*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.
 
*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:
 
*The imaginary units are  satisfy certain conditions:
−
*<math>i^2=j^2=k^2=ijk= -1</math>.
+
* <math>i^{2}=j^2=k^2=ijk= -1</math>.
−
*<math>i*j =k=−j*i</math>,<math>j*k = i = −k*j</math>, <math>k*i = j = −i*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\sdot k </math>
 +
 
 +
==Examples==
 +
#QUATERNION(9,2,3,4) = 9 2 3 4
 +
#QUATERNION(8,-2,4,-5) = 8 -2 4 -5
 +
#QUATERNION(-9,-12,-16,-20) = -9 -12 -16 -20
 +
 
 +
==Related Videos==
 +
 
 +
{{#ev:youtube|v=ln3vI4JEArc|280|center|Quaternion}}
 +
 
 +
==See Also==
 +
*[[Manuals/calci/QUARTILE  | QUARTILE ]]
 +
*[[Manuals/calci/TOQUARTER  | TOQUARTER ]]
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
*[[ Z3 |  Z3 home ]]
 +
 
 +
==References==
 +
[http://math.ucr.edu/~huerta/introquaternions.pdf Quartenion]
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 16:06, 30 November 2018

QUATERNION (a,b,c,d)


  • and 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 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 -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

Related Videos

Quaternion

See Also

References

Quartenion

Retrieved from "http://wiki.zcubes.com/index.php?title=Manuals/calci/QUATERNION&oldid=211406"