Special Matrices

A square matrix:

This is a matrix of order m × m. This simply means that number of rows equal to the number of columns.

\( \scriptsize \begin{pmatrix} 1 & 2 & 5 \\ 6 & 8 & 9 \\ 1 & 7 & 4\end{pmatrix} \)

This is a 3 × 3 matrix.

Diagonal matrix:

This is a square matrix with all elements zero except those on the leading diagonal.

\( \scriptsize \begin{pmatrix} 5 & 0 & 0 \\ 0 & 8 & 0 \\ 0 & 0 & 4 \end{pmatrix} \)

Unit matrix:

This is a diagonal matrix in which the elements on the leading diagonal are all unity.

\( \scriptsize \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \)

The unit matrix is denoted by I.

Null matrix:

A null matrix or simply zero matrix is one whose elements are all zero and is denoted by 0.

\( \scriptsize \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{pmatrix} \)