What is Upper Triangular Matrix? Determinant & Examples

Upper triangular matrix is a square matrix whose lower off-diagonal elements are zero. It is usually denoted by the capital letter ‘U‘.

Contents

A square matrix P = [xij] is said to be upper triangular matrix (UTM) if xij = 0 when i > j.

Note: In such matrix, the diagonal and/or upper off-diagonal elements may or may not be zero.

Upper triangular matrix examples

The example of UTM of order 3 (or matrix size is 3 x 3) is given below.

The example of UTM of order 2 (or matrix size is 2 x 2) is given below.

Upper triangular matrix determinant

The determinant of an upper triangular matrix is the product of its diagonal elements.

Let us understand by taking an example. Suppose U is an upper triangular matrix given as

Then the determinant of this matrix U is calculated as the product of the diagonal elements. Here, in this case, the diagonal elements are 7, 6 and 3. So the determinant is equal to 7 × 6 × 3 = 126.

i.e. |U| = 7 × 6 × 3 = 126

This site uses Akismet to reduce spam. Learn how your comment data is processed.

error: Content is protected !!

We don't have any banner, Flash, animation, obnoxious sound, or popup ad. We do not implement these annoying types of ads!

We need fund to operate the site, and almost all of it comes from our online advertising.