Matrix : A $m\times n$ matrix is a rectangular arrangement of $m\cdot n$ numbers into $m$ rows and $n$ columns. For example $\begin{pmatrix}1&2&3\\4&5&6\\\end{pmatrix}$ is a $3\times 2$ matrix. $A_{ij}$ refers to the element of $A$ in the i-th row and j-th column.

Number : A number $x$ is a mathematical symbol representing a quantity.

Matrix : A $m\times n$ matrix is a rectangular arrangement of $m\cdot n$ numbers into $m$ rows and $n$ columns. For example $\begin{pmatrix}1&2&3\\4&5&6\\\end{pmatrix}$ is a $3\times 2$ matrix. $A_{ij}$ refers to the element of $A$ in the i-th row and j-th column.

Dimension : The dimension of a vector space is the number of vectors in a basis of that vector space. It represent the minimum number of coordinates to uniquely describe any vector in the vector space. For example the dimension of $\mathbb{R}^2$ is 2.

Number : A number $x$ is a mathematical symbol representing a quantity.

Vector : Most commonly vector refers to a matrix with one column $\begin{pmatrix}x_1\\ \vdots \\x_n\\\end{pmatrix}.$ In general a vector is an element of a vector space.