# Manuals/calci/TRIANGULAR

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:
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",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

Triangular Matix