Symmetric Matrix

In this lesson, we will delve into the concept of a symmetric matrix.

A symmetric matrix is defined as a square matrix in which the elements in symmetric positions with respect to the main diagonal possess identical values. In mathematical notation, this can be expressed as follows: $$ a_{ij} = a_{ji} $$

To illustrate this concept, let's consider an example.

We have a square matrix with dimensions 3 rows by 3 columns.

Observe the main diagonal of the matrix, which consists of the elements a₁₁=5, a₂₂=4, a₃₃=7.

Next, let's examine the remaining elements above and below the diagonal.

You'll notice that the elements with symmetric indices, relative to the main diagonal, exhibit the same values.

This characteristic confirms that the matrix is indeed symmetric.

If you find this topic intriguing, we encourage you to continue following our lessons on linear algebra.