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}) = | + | *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". | ||
==Examples== | ==Examples== | ||
| − | + | 1. | |
| + | SKEWSYMMETRIC(4) | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 18: | Line 19: | ||
|39 || 0 || 15 || 72 | |39 || 0 || 15 || 72 | ||
|- | |- | ||
| − | |-2 || -15 || 0 ||43 | + | |(-2) || -15 || 0 ||43 |
|- | |- | ||
| − | |-25 || -72 || -43 || 0 | + | |(-25) || -72 || -43 || 0 |
|} | |} | ||
| + | 2. | ||
| + | SKEWSYMMETRIC(9) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 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== | ||
| + | |||
| + | {{#ev:youtube|v=uKPmyG18N7I|280|center|Skew Symmetric}} | ||
| + | |||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/KURT| KURT]] | ||
| + | *[[Manuals/calci/STDEV | STDEV ]] | ||
| + | *[[Manuals/calci/STDEVP | STDEVP ]] | ||
| + | |||
| + | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Skewness Skewness] | ||
| + | |||
| + | |||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 12:01, 25 April 2019
SKEWSYMMETRIC(Order)
- is the order of the skew symmetric matrix.
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".
,where 
is the matrix transpose.
row and 
column is 
.
then the skew symmetric condition is 
= 
.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
See Also
References