Lesson plan
Commuting matrices
In linear algebra, two matrices A and B are said to commute if AB=BA , or equivalently if their commutator [A,B]= AB-BA is zero. Matrices A that commute with matrix B are called the commutant of matrix B (and vice versa). A set of matrices A_1, \ldots, A_k is said to commute if they commute pairwise, meaning that every pair of matrices in the set commutes.
Article summary
In linear algebra, two matrices A and B are said to commute if AB=BA , or equivalently if their commutator [A,B]= AB-BA is zero. Matrices A that commute with matrix B are called the commutant of matrix B (and vice versa). A set of matrices A_1, \ldots, A_k is said to commute if they commute pairwise, meaning that every pair of matrices in the set commutes.
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Discussion questions
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- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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