Difference between revisions of "Manuals/calci/TRIANGULAR"
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==Examples== | ==Examples== | ||
| − | *1.MATRIX("triangular") | + | *1.MATRIX("triangular",3) |
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| 0 || 0 || 84 | | 0 || 0 || 84 | ||
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| − | *4.MATRIX("lower-triangular") | + | *4.MATRIX("lower-triangular",4) |
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|25 || -18 || 12 || 40 | |25 || -18 || 12 || 40 | ||
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| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|7-jSS6f_urg|280|center|Triangular Matix}} | ||
==See Also== | ==See Also== | ||
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==References== | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Triangular_matrix Triangular Matrix] | ||
| + | *[http://mathworld.wolfram.com/UpperTriangularMatrix.html Upper Triangular Matrix] | ||
| + | *[http://mathworld.wolfram.com/LowerTriangularMatrix.html Lower Triangular Matrix] | ||
Latest revision as of 01:44, 26 October 2015
MATRIX("TRIANGULAR",order)
- is the size of the Triangular matrix.
is the size of the Triangular matrix.Description
- This function gives a triangular matrix of order 3.
- A square matrix is called triangular matrix if that matrix is an upper triangular matrix or lower triangular matrix.
- A square matrix is called lower triangular if all the entries above the main diagonal are zero.
- Similarly, a square matrix is called upper triangular if all the entries below the main diagonal are zero.
- So a triangular matrix is a special kind of square matrix.
- A triangular matrix is one that is either lower triangular or upper triangular.
- Some matrices, such as the identity matrix, are both upper and lower triangular.
- A matrix is upper and lower triangular simultaneously if and only if it is a diagonal matrix.
- Also lower triangular matrix is called left triangular matrix and upper triangular matrix is called right triangular matrix.
- Triangular matrices have the following properties:
- The inverse of a triangular matrix is a triangular matrix.
- The product of two triangular matrices is a triangular matrix.
- The determinant of a triangular matrix is the product of the diagonal elements.
- The eigenvalues of a triangular matrix are the diagonal elements.
- In calci, MATRIX("triangular") gives the triangular matrix of order 3.
- MATRIX("uppertriangular") or MATRIX("upper-triangular") gives the upper triangular matrix of oreder 3.
- Also MATRIX("lowertriangular") or MATRIX("lower-triangular") is showing the lower triangular matrix of order 3.
- So in Calci, users can get the different types of triangular matrices with the different orders.
Examples
- 1.MATRIX("triangular",3)
| 15 | -96 | -53 |
| 0 | 94 | 0 |
| 0 | 0 | 77 |
- 2.MATRIX("triangular",6)
| 49 | 0 | 0 | 0 | 0 | 0 |
| 55 | 93 | 0 | 0 | 0 | 0 |
| -30 | -42 | 48 | 0 | 0 | 0 |
| -82 | 48 | -9 | 62 | 0 | 0 |
| -6 | -37 | -68 | -6 | -7 | 0 |
| 36 | 62 | 28 | -96 | 18 | 55 |
- 3.MATRIX("uppertriangular")
| -54 | 24 | 28 |
| 0 | -9 | 79 |
| 0 | 0 | 84 |
- 4.MATRIX("lower-triangular",4)
| 16 | 0 | 0 | 0 |
| -66 | -17 | 0 | 0 |
| 69 | -93 | -6 | 0 |
| 25 | -18 | 12 | 40 |