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I have a set of (about 100) general real square matrices. Is it possible to determine whether none of their linear combinations has complex eigenvalues?

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    Nothing special about these "general real square matrices"?2012-08-04
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    perhaps, they have real eigenvalues2012-08-04
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    First of all, choose a basis of the space of linear combinations, so you'll have to work with fewer matrices.2012-08-04
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    Do the matrices have any other properties? they commute?2012-08-04
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    they are no other special properties, they do not commute, some of them are singular (1 or 2 eigenvalues are zero)2012-08-04

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