The sum of nonsingular matrices is often nonsingular
classification
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nonsingularmatricesapplicationgeneralmanyoftenpairsprove
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If $M$ is a set of nonsingular $k\times k$ matrices then for many pairs of matrices, $A,B\in M,$ the sum is nonsingular, $\det(A+B)\neq 0.$ We prove a more general statement on nonsingular sums with an application.
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