# Triangular Matrix Calculator Online

### Explanation:

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.

Triangular Matrix Example Image:

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