A square matrix is referred to as a triangular matrix if all of the components below and/or above the
main diagonal are zeros. There are primarily two categories of triangular matrices.
Lower triangular matrices are those square matrices that have zeros for every member above the major
diagonal.
Upper triangular matrices are square matrices with all of their elements zero below the principal diagonal.
What is Triangular Matrix?
The set of matrices includes a special type of square matrix called a triangular matrix. Triangular matrices come
in two varieties: lower and upper triangular matrices.
When every element above a square matrix's primary diagonal is zero, the matrix is referred to as a lower
triangular matrix.
If every component below the primary diagonal is zero, a square matrix is referred to as an upper triangular
matrix.
Following is a sample of a triangular matrix:
Upper Triangular Matrix Example:
A =
2
-1
3
0
5
2
0
0
-2
Now in the above given matrix, the matrix is in upper triangular form because it all of the entries below the
main diagonal are zero.
Lower Triangular Matrix Example:
A =
2
0
0
1
5
0
1
-1
-2
Now in the above given matrix, the matrix is in lower triangular form because it all of the entries above the
main diagonal are zero.
Properties of Triangular Matrix:
Now that we are clear on what a triangular matrix is, let's go over some of its key characteristics. A
triangular matrix's characteristics are listed below:
A triangular matrix has a triangular transposition as well.
An upper triangular matrix is a lower triangular matrix's transpose, and vice versa.
A triangular matrix is created when two triangular matrices are multiplied.
If and only if the major diagonal's entries are all non-zero, a triangular matrix is invertible.
A lower(upper) triangular matrix is the result of multiplication f otwo other lower(upper) triangular
matrices.
A triangular matrix has a triangular inverse as well.
The product of the major diagonal's elements is a triangular matrix's determinant.
How to use check Triangular Matrix Calculator?
Firstly, you need to enter the dimension of the matrix. Enter number of rows in "Rows" input field
and Enter number of columns in "Columns" input field.
Then press the button "Set Matrix".
An empty matrix will appear below and then you can enter your values inside the matrix.
After entering all the values press "Solve" button, the result will automatically appear below which
check whether the matrix is Triangular Matrix or not.
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