A square matrix is a matrix where the number of rows equals the number of columns, that is, (n=k).
The diagonal numbers of a square matrix are the numbers of a matrix where the row number equals the column number, for example, (a_{11}), (a_{22}), and so on. A diagonal matrix is a square matrix where all non-diagonal numbers are equal to 0. For example, begin{equation*} mathbf{A}=left( begin{array}{ccc} -1 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 3 end{array} right) . end{equation*}
An identity matrix is a diagonal matrix where all the diagonal numbers are equal to 1. This special matrix is often denoted by (mathbf{I}).
A symmetric matrix is a square matrix (mathbf{A}) such that the matrix remains unchanged if we interchange the roles of the rows and columns. More formally, a matrix (mathbf{A}) is symmetric if (mathbf{A=A} ^{prime }). For example, begin{equation*} mathbf{A}=left( begin{array}{ccc} 1 & 2 & 3 \ 2 & 4 & 5 \ 3 & 5 & 10 end{array} right) mathbf{=A}^{prime }. end{equation*} Note that a diagonal matrix is a symmetric matrix.