> [!summary] The rank of a matrix is the number of pivots >[!info]+ Read Time **⏱ 1 min** # Definition The rank of a [[Matrix Notation|matrix]] is the number of [[Leading 1s|leading 1s]] in its [[Row Echelon Form|row echelon form]] (not necessarily [[Reduced Row Echelon Form|RREF]]). The rank describes the number of [[Linear Independence & Dependence|linearly independent]] [[Row & Columns Vectors|column vectors]] in a matrix. A matrix in [[Row Echelon Form|REF]] or [[Reduced Row Echelon Form|RREF]] will always have a rank greater than 1. Upset the [[Zero Matrix|zero matrix]], which has a rank of 0. If a matrix is denoted as $A$, the rank of the matrix is denoted as $\text{rank(A)}$ # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/cSj82GG6MX4?si=9TMO3YX9JEnIw6Ue" 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>