What is Lower Triangular Matrix? Determinant & Examples

Lower triangular matrix is a square matrix whose upper off-diagonal elements are zero. It is usually denoted by the capital letter ‘L‘.

A square matrix Q = [xij] is said to be lower triangular matrix (LTM) if xij = 0 when i < j.

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

Lower triangular matrix examples

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

    \[L=\begin{bmatrix} 6 &0 &0 \\ -4& 8 &0 \\ 2&3 & 6 \end{bmatrix}\]

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

    \[L=\begin{bmatrix} 1 &0 \\ 4& 2 \end{bmatrix}\]

Lower triangular matrix determinant

The determinant of a lower triangular matrix is the product of its diagonal elements.

Let us understand by taking an example. Suppose L is a lower triangular matrix given as

    \[L=\begin{bmatrix} 4 &0 &0 \\ -4& 3 &0 \\ 2&3 & 2 \end{bmatrix}\]

Then the determinant of this matrix L is calculated as the product of the diagonal elements. Here, in this case, the diagonal elements are 4, 3 and 2. So the determinant is equal to 4 × 3 × 2 = 24.

i.e. |L| = 4 × 3 × 2 = 24

Leave a Comment

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

error: Content is protected !!

Adblocker detected! Please consider reading this notice.

We've detected that you are using AdBlock Plus or some other adblocking software which is preventing the page from fully loading.

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.

Please add electricalvoice.com to your ad blocking whitelist or disable your adblocking software.