Difference between revisions of "Manuals/calci/SKEWSYMMETRIC"
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*i.e.<math>A = (a_{ij})</math> then the skew symmetric condition is <math>(a_{ij}) = −(a_{ij})</math>. | *i.e.<math>A = (a_{ij})</math> then the skew symmetric condition is <math>(a_{ij}) = −(a_{ij})</math>. | ||
*So its diagonal values are "0". | *So its diagonal values are "0". | ||
| + | |||
| + | ==Examples== | ||
| + | #SKEWSYMMETRIC(4) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || -39|| 2 || 25 | ||
| + | |- | ||
| + | |39 || 0 || 15 || 72 | ||
| + | |- | ||
| + | |-2 || -15 || 0 ||43 | ||
| + | |- | ||
| + | |-25 || -72 || -43 || 0 | ||
| + | |} | ||
Revision as of 15:02, 20 December 2016
SKEWSYMMETRIC(Order)
- 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 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 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=A^T} ,where 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^T} is the matrix transpose.
- If the entry in the 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^{th}} row 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 j^{th}} column is 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_{ij}} .
- i.e.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 = (a_{ij})} then the skew symmetric condition is 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_{ij}) = −(a_{ij})} .
- So its diagonal values are "0".
Examples
- SKEWSYMMETRIC(4)
| 0 | -39 | 2 | 25 |
| 39 | 0 | 15 | 72 |