Manuals/calci/TRIANGULAR

MATRIX("TRIANGULAR",order)

• $order$ 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:

1. The inverse of a triangular matrix is a triangular matrix.
2. The product of two triangular matrices is a triangular matrix.
3. The determinant of a triangular matrix is the product of the diagonal elements.
4. 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")

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")

16	0	0	0
-66	-17	0	0
69	-93	-6	0
25	-18	12	40

See Also

• PERSYMMETRIC
• PASCAL
• HANKEL