# What is matrix rank and how do i calculate it?

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The rank of a matrix $A$ is the number of independent columns of $A$. A square matrix is full rank if all of its columns are independent. That is, a full rank matrix has no column vector $v_{i}$ of $A$ that can be expressed as a linear combination of the other column vectors $v_{j}\neq \Sigma _{{i=0,i\neq j}}^{{n}}a_{i}v_{i}$.