> [!summary] A matrix has rows and columns. The row vectors are the sub-matrix of a certain row. The column vector sub-matrix of a certain column >[!info]+ Read Time **⏱ 1 min** # Definition Row and column vectors come from an $m\times n$ [[Matrix Notation|matrix]] denoted at $A$ below $ A = \left[ \begin{array}{cccc} a_{11} & a_{12} & \cdots & a_{1 n} \\ a_{21} & a_{22} & \cdots & a_{2 n}\\ \vdots & \vdots & \ddots & \vdots \\ a_{m 1} & a_{m 2} & \cdots & a_{mn} \end{array} \right] $ The row vectors denoted as $r$ are formed from the rows of $A$ with $n$ columns $ \begin{array}{c} r_{1}=\begin{bmatrix} a_{11} & a_{12} & \dots & a_{1n} \end{bmatrix} \\ \\ r_{2}= \begin{bmatrix} a_{21} & a_{22} & \cdots & a_{2 n} \\ \end{bmatrix} \\ \\ r_{m} = \begin{bmatrix} a_{m 1} & a_{m 2} & \cdots & a_{mn} \end{bmatrix} \end{array} $ These vectors are $\mathbb{R}^n$ since each row vector has $n$ entries The column vectors denoted as $c$ are formed from the columns of $A$ with $m$ rows $ c_{1} = \begin{bmatrix} a_{11} \\ a_{21} \\ \vdots \\ a_{m_{1}} \end{bmatrix}, \quad c_{2} = \begin{bmatrix} a_{12} \\ a_{22} \\ \vdots \\ a_{m_{2}} \end{bmatrix}, \quad c_{n} = \begin{bmatrix} a_{1n} \\ a_{2n} \\ \vdots \\ a_{mn} \end{bmatrix} $ These vectors are in $\mathbb{R}^m$ since each column vectors has $m$ entries # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/YtG1gRISbBQ?si=f2W6neb2GpUuBJ7z" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>