Commuting matrices

In linear algebra, two matrices ${\displaystyle A}$ and ${\displaystyle B}$ are said to commute if ${\displaystyle AB=BA}$, or equivalently if their commutator ${\displaystyle [A,B]=AB-BA}$ is zero. Matrices ${\displaystyle A}$ that commute with matrix ${\displaystyle B}$ are called the commutant of matrix ${\displaystyle B}$ (and vice versa).

A set of matrices ${\displaystyle A_{1},\ldots ,A_{k}}$ is said to commute if they commute pairwise, meaning that every pair of matrices in the set commutes.