Some Special Matrices

Square matrix: Same number of rows and columns ($n\times n$).

Identity matrix, $I_{n \times n}$: \begin{eqnarraystar} I[i,j] & = & \left \{ \begin{array} {lll} 1 \;\; & \;\; ... ... \ \ 0 \;\; & \;\; \mbox{otherwise} \end{array} \right. \end{eqnarraystar}

Diagonal matrix, $D_{n \times n}$ \begin{eqnarraystar} D[i,j] & = & 0 \;\;\;\; \mbox{if} \;\; i \neq j \end{eqnarraystar}

Tridiagonal matrices, $T_{n \times n}$ \begin{eqnarraystar} T[i,j] & = & 0 \;\;\;\; \mbox{if} \;\; \vert i - j\vert \gt 1 \end{eqnarraystar}

Lower-triangular matrices, $L_{n \times n}$ \begin{eqnarraystar} L[i,j] & = & 0 \;\;\;\; \mbox{if} \;\; i < j \end{eqnarraystar}

Upper-triangular matrices, $U_{n \times n}$ \begin{eqnarraystar} U[i,j] & = & 0 \;\;\;\; \mbox{if} \;\; i \gt j \end{eqnarraystar}

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