A commutation matrix, often denoted as \(C\), is a specific type of permutation matrix that is used in linear algebra, particularly in the context of vector and matrix operations. The primary role of the commutation matrix is to facilitate the rearrangement of the elements of a vector or to convert a matrix into a different form. ### Definition For a given vector or matrix, the commutation matrix rearranges the elements when it is multiplied by the vector or applied to the matrix.
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