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Almost commuting matrices, i.e. matrices with a sufficiently small commutator, may be nearly commuting, i.e. there may exist matrices close by which do commute. By referencing current literature, this condition

Almost commuting matrices, i.e. matrices with a sufficiently small commutator, may be nearly commuting, i.e. there may exist matrices close by which do commute. By referencing current literature, this condition is studied for fixed dimension, unitary, self-adjoint, and orthogonal matrices. These proofs are made more accessible and compared to each other, providing insight to possible future progress in the field.

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  • 2015-05
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