Difference between revisions of "Manuals/calci/SKEWSYMMETRIC"

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*A Skew Symmetric is a square matrix which satisfies the following identity <math>A=A^T</math>,where <math>A^T</math> is the matrix transpose.  
 
*A Skew Symmetric is a square matrix which satisfies the following identity <math>A=A^T</math>,where <math>A^T</math> is the matrix transpose.  
 
*If the entry in the <math>i^{th}</math> row and <math>j^{th}</math> column is <math>a_{ij}</math>.
 
*If the entry in the <math>i^{th}</math> row and <math>j^{th}</math> column is <math>a_{ij}</math>.
*i.e.<math>A = (a_{ij})</math> then the skew symmetric condition is <math>(a_{ij}) = (a_{ij})</math>.  
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*i.e.<math>A = (a_{ij})</math> then the skew symmetric condition is <math>(a_{ij})</math> = <math>-(a_{ij})</math>.
 
*So its diagonal values are "0".
 
*So its diagonal values are "0".
  
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| (-70) || -45 || 43 || -70 || -34 || 0 || -55 || -76 || 0
 
| (-70) || -45 || 43 || -70 || -34 || 0 || -55 || -76 || 0
 
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|}
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==Related Videos==
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{{#ev:youtube|v=uKPmyG18N7I|280|center|Skew Symmetric}}
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==See Also==
 
==See Also==
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==References==
 
==References==
 
*[http://en.wikipedia.org/wiki/Skewness Skewness]
 
*[http://en.wikipedia.org/wiki/Skewness Skewness]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 13:01, 25 April 2019

SKEWSYMMETRIC(Order)


  • is the order of the skew symmetric matrix.

Description

  • This function shows the Skew Symmetric matrix with the given order.
  • Skew Symmetric is also called Anti Symmetric or Antimetric.
  • A Skew Symmetric is a square matrix which satisfies the following identity ,where is the matrix transpose.
  • If the entry in the row and column is .
  • i.e. then the skew symmetric condition is = .
  • So its diagonal values are "0".

Examples

1. SKEWSYMMETRIC(4)

0 -39 2 25
39 0 15 72
(-2) -15 0 43
(-25) -72 -43 0

2. SKEWSYMMETRIC(9)

0 48 -36 72 25 51 -13 -98 70
(-48) 0 -97 -33 78 -30 -56 62 45
36 97 0 42 -47 58 94 24 -43
(-72) 33 -42 0 -23 -77 -80 69 70
(-25) -78 47 23 0 -17 17 -100 34
(-51) 30 -58 77 17 0 -43 -67 0
13 56 -94 80 -17 43 0 -24 55
98 -62 -24 -69 100 67 24 0 76
(-70) -45 43 -70 -34 0 -55 -76 0

Related Videos

Skew Symmetric


See Also

References