MATRIX("TRIANGULAR",order)
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
| 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")
- 4.MATRIX("lower-triangular",4)
| 16 |
0 |
0 |
0
|
| -66 |
-17 |
0 |
0
|
| 69 |
-93 |
-6 |
0
|
| 25 |
-18 |
12 |
40
|
See Also
References