Difference between revisions of "Manuals/calci/ANTIDIAGONAL"
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| − | <div style="font-size:30px">''' | + | <div style="font-size:30px">'''MATRIX("ANTI-DIAGONAL",order)'''</div><br/> |
| + | *<math> order </math> is the order of the Anti diagonal matrix. | ||
| + | |||
| + | ==Description== | ||
| + | *This function gives the matrix satisfying the anti diagonal properties. | ||
| + | *An anti-diagonal matrix is a matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner <math>\nearrow</math>, known as the anti-diagonal. | ||
| + | *So here we are getting all entries are 0 except from the opposite of main diagonal as 1. | ||
| + | *The properties of anti diagonal matrix are: | ||
| + | *1.The product of two anti-diagonal matrices is a diagonal matrix. | ||
| + | *2. If A and D are n×n anti-diagonal and diagonal matrices, respectively, then AD,DA are anti-diagonal. | ||
| + | *3.All anti-diagonal matrices are also persymmetric. | ||
| + | *Here MATRIX("anti-diagonal") displays the antidiagonal matrix of order 3. | ||
| + | *To display the different order of matrices then the syntax is MATRIX("anti-diagonal",5). | ||
| + | |||
| + | ==Examples== | ||
| + | *MATRIX("ANTI-DIAGONAL") | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || 0 || 1 | ||
| + | |- | ||
| + | | 0 || 1 || 0 | ||
| + | |- | ||
| + | | 1 || 0 || 0 | ||
| + | |} | ||
| + | *MATRIX("anti-diagonal",4,200..204) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || 0 || 0 || 200 | ||
| + | |- | ||
| + | | 0 || 0 || 201 || 0 | ||
| + | |- | ||
| + | | 0 || 202 || 0 || 0 | ||
| + | |- | ||
| + | | 203 || 0 || 0 || 0 | ||
| + | |} | ||
| + | *MATRIX("anti-diagonal",3,-32.05) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 0 || 0 || -32.05 | ||
| + | |- | ||
| + | | 0 || -32.05 || 0 | ||
| + | |- | ||
| + | | -32.05 || 0 || 0 | ||
| + | |} | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/ARROWHEAD| ARROWHEAD]] | ||
| + | *[[Manuals/calci/MATRIXOPERATORS| MATRIXOPERATORS]] | ||
| + | |||
| + | ==References== | ||
Revision as of 08:49, 17 April 2015
MATRIX("ANTI-DIAGONAL",order)
- is the order of the Anti diagonal matrix.
is the order of the Anti diagonal matrix.Description
- This function gives the matrix satisfying the anti diagonal properties.
- An anti-diagonal matrix is a matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner , known as the anti-diagonal.
- So here we are getting all entries are 0 except from the opposite of main diagonal as 1.
- The properties of anti diagonal matrix are:
- 1.The product of two anti-diagonal matrices is a diagonal matrix.
- 2. If A and D are n×n anti-diagonal and diagonal matrices, respectively, then AD,DA are anti-diagonal.
- 3.All anti-diagonal matrices are also persymmetric.
- Here MATRIX("anti-diagonal") displays the antidiagonal matrix of order 3.
- To display the different order of matrices then the syntax is MATRIX("anti-diagonal",5).
, known as the anti-diagonal.Examples
- MATRIX("ANTI-DIAGONAL")
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
- MATRIX("anti-diagonal",4,200..204)
| 0 | 0 | 0 | 200 |
| 0 | 0 | 201 | 0 |
| 0 | 202 | 0 | 0 |
| 203 | 0 | 0 | 0 |
- MATRIX("anti-diagonal",3,-32.05)
| 0 | 0 | -32.05 |
| 0 | -32.05 | 0 |
| -32.05 | 0 | 0 |