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

commuting pair, as discussed at commuting matrices. As for a single matrix, over the complex numbers these can be triangularized by unitary matrices....

ring, algebraic structures with the commutative property Commuting matrices, sets of matrices whose products do not depend on the order of multiplication...

A} and B {\displaystyle B} : consists only of matrices similar to a diagonal matrix, or has no matrices in it similar to a diagonal matrix, or has exactly...

In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are Hermitian, involutory and unitary. Usually...

function satisfies ex+y = ex ey. The same is true for commuting matrices. If matrices X and Y commute (meaning that XY = YX), then, e X + Y = e X e Y . {\displaystyle...

radius of a product of commuting matrices: if A 1 , … , A n {\displaystyle A_{1},\ldots ,A_{n}} are matrices that all commute, then ρ ( A 1 ⋯ A n ) ≤...

Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. This article...

eigenvalues to form singular values. Among complex matrices, all unitary, Hermitian, and skew-Hermitian matrices are normal, with all eigenvalues being unit...

conventions: matrices are represented by capital letters in bold, e.g. A; vectors in lowercase bold, e.g. a; and entries of vectors and matrices are italic...