Difference between revisions of "Manuals/calci/SKEWSYMMETRIC"
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| Line 18: | Line 18: | ||
|39 || 0 || 15 || 72 | |39 || 0 || 15 || 72 | ||
|- | |- | ||
| − | |-2 || -15 || 0 ||43 | + | |(-2) || -15 || 0 ||43 |
|- | |- | ||
| − | |-25 || -72 || -43 || 0 | + | |(-25) || -72 || -43 || 0 |
|} | |} | ||
Revision as of 15:03, 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 |
| (-2) | -15 | 0 | 43 |
| (-25) | -72 | -43 | 0 |