Difference between revisions of "Manuals/calci/HOLLOW"
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| − | <div style="font-size:30px">'''HOLLOW'''</div><br/> | + | <div style="font-size:30px">'''MATRIX("HOLLOW",order)'''</div><br/> |
| + | *<math>order</math> is the order of the Hollow matrix. | ||
| + | |||
| + | ==Description== | ||
| + | *This function shows the matrix of order 3 with the hollow matrix property. | ||
| + | *A hollow matrix may be a square matrix whose diagonal elements are all equal to zero. | ||
| + | *The real skew-symmetric matrix,adjacency matrix of a finite simple graph and a distance matrix or Euclidean matrix are some examples of Hollow matrix. | ||
| + | *In Calci, users can get different type of hollow matrices. | ||
| + | *For example, to get negative decimal places of hollow matrix is MATRIX("hollow:negative") and to get positive decimal places is MATRIX("hollow:positive"). | ||
| + | *Also MATRIX("hollow:negzeropos") is used to get a hollow ineteger matrix with the numbers 0,1 and -1. | ||
| + | *MATRIX("hollow:integer") is used to get any integer numbers of Hollow matrix. | ||
| + | |||
| + | ==Examples== | ||
| + | *1.MATRIX("hollow",4) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || -20 || -48 || -31 | ||
| + | |- | ||
| + | | 22 || 0 || 62 || 75 | ||
| + | |- | ||
| + | | 64 || 6 || 0 || 2 | ||
| + | |- | ||
| + | | 41 || 6 || -51 ||0 | ||
| + | |} | ||
| + | *2.MATRIX("hollow:positive",3) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || 17.894603312015533 || 43.48729630000889 | ||
| + | |- | ||
| + | | 57.917751371860504 || 0 ||56.09508000779897 | ||
| + | |- | ||
| + | | 92.90755833499134 || 14.018815965391695 || 0 | ||
| + | |} | ||
| + | *3.MATRIX("hollow:negative",3) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || -76.5736571745947 ||-19.65819902252406 | ||
| + | |- | ||
| + | | -52.96719539910555 || 0 ||-83.0037885112688 | ||
| + | |- | ||
| + | | -72.52066603396088 || -66.49071478750557 || 0 | ||
| + | |} | ||
| + | *4.MATRIX("hollow:negzeropos",5) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || 0 || 0 || -1 || 1 | ||
| + | |- | ||
| + | |1 || 0 ||-1 || -1 ||1 | ||
| + | |- | ||
| + | |0 || -1 || 0 || 1 || 1 | ||
| + | |- | ||
| + | |1 || -1 || 1 || 0 || -1 | ||
| + | |- | ||
| + | |0 || 1 || -1 || 0 ||0 | ||
| + | |} | ||
| + | *5.MATRIX("hollow:integer",7) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || 92 || 96 || -46 || 40 || -100 || -86 | ||
| + | |- | ||
| + | | -92 || 0 ||-37 || 64 || -20 || 52 || -5 | ||
| + | |- | ||
| + | | -74 || 54 || 0 || -70 || 12 || 50 || 7 | ||
| + | |- | ||
| + | |32 || 9 || 43 || 0 || -48 || 76 || -76 | ||
| + | |- | ||
| + | | -26 || 73 || 97 || -34 ||0 || -91 || -91 | ||
| + | |- | ||
| + | | -90 || 36 || -84 || 70 || -60 || 0 ||86 | ||
| + | |- | ||
| + | | -42 || 9 ||8 || -75 ||-40 || -82 ||0 | ||
| + | |} | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/HADAMARD| HADAMARD]] | ||
| + | *[[Manuals/calci/HESSENBERG| HESSENBERG]] | ||
| + | *[[Manuals/calci/CIRCULANT| CIRCULANT]] | ||
| + | *[[Manuals/calci/HANKEL| HANKEL]] | ||
| + | |||
| + | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Hollow_matrix Hollow matrix] | ||
Latest revision as of 01:15, 26 October 2015
MATRIX("HOLLOW",order)
- is the order of the Hollow matrix.
is the order of the Hollow matrix.Description
- This function shows the matrix of order 3 with the hollow matrix property.
- A hollow matrix may be a square matrix whose diagonal elements are all equal to zero.
- The real skew-symmetric matrix,adjacency matrix of a finite simple graph and a distance matrix or Euclidean matrix are some examples of Hollow matrix.
- In Calci, users can get different type of hollow matrices.
- For example, to get negative decimal places of hollow matrix is MATRIX("hollow:negative") and to get positive decimal places is MATRIX("hollow:positive").
- Also MATRIX("hollow:negzeropos") is used to get a hollow ineteger matrix with the numbers 0,1 and -1.
- MATRIX("hollow:integer") is used to get any integer numbers of Hollow matrix.
Examples
- 1.MATRIX("hollow",4)
| 0 | -20 | -48 | -31 |
| 22 | 0 | 62 | 75 |
| 64 | 6 | 0 | 2 |
| 41 | 6 | -51 | 0 |
- 2.MATRIX("hollow:positive",3)
| 0 | 17.894603312015533 | 43.48729630000889 |
| 57.917751371860504 | 0 | 56.09508000779897 |
| 92.90755833499134 | 14.018815965391695 | 0 |
- 3.MATRIX("hollow:negative",3)
| 0 | -76.5736571745947 | -19.65819902252406 |
| -52.96719539910555 | 0 | -83.0037885112688 |
| -72.52066603396088 | -66.49071478750557 | 0 |
- 4.MATRIX("hollow:negzeropos",5)
| 0 | 0 | 0 | -1 | 1 |
| 1 | 0 | -1 | -1 | 1 |
| 0 | -1 | 0 | 1 | 1 |
| 1 | -1 | 1 | 0 | -1 |
| 0 | 1 | -1 | 0 | 0 |
- 5.MATRIX("hollow:integer",7)
| 0 | 92 | 96 | -46 | 40 | -100 | -86 |
| -92 | 0 | -37 | 64 | -20 | 52 | -5 |
| -74 | 54 | 0 | -70 | 12 | 50 | 7 |
| 32 | 9 | 43 | 0 | -48 | 76 | -76 |
| -26 | 73 | 97 | -34 | 0 | -91 | -91 |
| -90 | 36 | -84 | 70 | -60 | 0 | 86 |
| -42 | 9 | 8 | -75 | -40 | -82 | 0 |