There are some important named types of matrices to memorize: - **Row Matrix**: a matrix that is one row $\begin{bmatrix}1 & 2 & 3 & 4\end{bmatrix}$ - **Column Matrix**: a matrix that is one column $\begin{bmatrix}1 \\ 2 \\ 3 \\ 4\end{bmatrix}$ - **Square Matrix**: a matrix with equal number of rows and columns $\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$ - **Identity Matrix**: a square matrix with the diagonal all being 1 and all other elements being 0. Denoted by $\mathbf{I}$. The identity matrix is useful because when any other matrix is multiplied by it is itself. $\mathbf{I}=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$ - **Zero Matrix**: a matrix with all elements being 0. $\mathbf{0}=\begin{bmatrix}0&0&0\\0&0&0\end{bmatrix}$ - **Diagonal Matrix**: a square matrix with all elements not on the main diagonal equal to 0 $\begin{bmatrix}2&0&0\\0&5&0\\0&0&1\end{bmatrix}$ - **Upper Triangular Matrix**: a square matrix with all elements below the main diagonal equal to 0 $\begin{bmatrix}2&1&3\\0&5&-1\\0&0&1\end{bmatrix}$ - **Lower Triangular Matrix**: a square matrix with all elements above the main diagonal equal to 0 $\begin{bmatrix}2&0&0\\1&5&0\\8&-3&1\end{bmatrix}$