# Rank (Matrices) > The **rank** of a matrix is the number of dimensions in the [Column Space](Column%20Space.md) of a matrix. Note that this is equivalent to the number of ***rows*** in a matrix. Remember, a matrix can be thought of as describing where the transformation it encodes takes the basis vectors. Each column represents the new description of a basis vector. So, the number of columns represents the dimensionality of the starting space, while the number of rows represents the number of dimensions in the output space. When the rank of a matrix is equivalent to it's number of output dimensions, it is referred to a **full rank**. If all of the columns of a matrix are [linearly dependent](Linear%20Dependence.md), it is a **rank 1** matrix.  --- Date: 20211229 Links to: [Linear Algebra MOC](Linear%20Algebra%20MOC.md) Tags: References: * [3b1b video](https://youtu.be/uQhTuRlWMxw?t=463)