Symmetric Matrix of Order N

A square matrix A of order n is said to be symmetric if [latex]a_{i,\space j}[/latex] = [latex]a_{j,\space i}[/latex] for [latex]i,\space j[/latex] ∈ {1, 2, 3, 4, ..., n}.

In a symmetric matrix, the main diagonal is a line of symmetry for the elements located on either side of the diagonal.

Example

The matrices A = [latex]\begin{pmatrix}–3 & 5\\5 & – 3\end{pmatrix}[/latex] and B = [latex]\begin{pmatrix}–3 & 5 & 6\\5 & 0 & 2\\6 & 2 & –1\end{pmatrix}[/latex] are symmetric matrices.

Symmetric Matrix of Order N

Example

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