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

Related Videos

Triangular Matix

See Also

References