Triangular Matrix | Upper Triangular Matrix

0
10


There are two types of triangular matrices.

1. Upper Triangular Matrix: A square matrix (aij)
is said to be an upper triangular matrix if all the elements below the principal
diagonal are zero (0). That is, [aij]m× n is an
upper triangular matrix if (i) m = n and (ii) aij = 0 for i > j.

Examples of an Upper Triangular Matrix are:

(i) (begin{bmatrix} 5 & 2 & 8\ 0 & 3 &
10\ 0 & 0 & 8 end{bmatrix})


(ii) (begin{bmatrix} -1 & 7 & 3\ 0 & 6 & 1\ 0 & 0 & 5 end{bmatrix})

(iii) (begin{bmatrix} 3 & 0 & 3\ 0 & 7 & -1\ 0 & 0 & 2 end{bmatrix})

2. Lower Triangular Matrix: A square matrix (aij)
is said to be a lower triangular matrix if all the elements above the principal
diagonal are zero (0). That is, [aij]m× n is a
lower triangular matrix if (i) m = n and (ii) aij = 0 for i < j.

Examples of a Lower Triangular Matrix are:

(i) (begin{bmatrix} 7 & 0 & 0\ 3 & 9 &
0\ 1 & 2 & 1 end{bmatrix})

(ii) (begin{bmatrix} 1 & 0 & 0\ -5 & 1 &
0\ 3 & 7 & 1 end{bmatrix})

(iii) (begin{bmatrix} 9 & 0 & 0\ 1 & 3 &
0\ 2 & 5 & -4 end{bmatrix})

Definition of Triangular
Matrix:

A square matrix is said to be a triangular matrix if it is
either upper triangular or lower triangular.

For example:

(i) (begin{bmatrix} 2 & 3 & 1\ 0 & 1 &
3\ 0 & 0 & 4 end{bmatrix})

(ii) (begin{bmatrix} 1 & 0 & 0\ 2 & 3 &
0\ 4 & 1 & 2 end{bmatrix})

(iii) (begin{bmatrix} 0 & 0 & 0\ 3 & 0 &
0\ 2 & 1 & 0 end{bmatrix})

(iv) (begin{bmatrix} 0 & 1 & 2\ 0 & 0 &
3\ 0 & 0 & 0 end{bmatrix})

A diagonal matrix is both upper triangular and lower
triangular.

`

10th Grade Math

From Triangular Matrix to HOME


Didn’t find what you were looking for? Or want to know more information
about
Math Only Math.
Use this Google Search to find what you need.








Source link

LEAVE A REPLY

Please enter your comment!
Please enter your name here