Triangular Matrix Calculator Online


Triangular Matrix Description


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:

    Triangular Matrix example


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