A Bohemian matrix family is a set of matrices whosefree entries come from a single discrete, usually finite population, denoted here by P. That is, each entry of any matrix from this particular Bohemian matrix family must be an element of P. Such a matrix is called a Bohemian matrix. Bohemian matrices can have other structures as well, such as being a Toeplitz matrix or an upper Hessenberg matrix. Usually, only one Bohemian matrix family with a fixed population P is studied at a time, and so one can classify any given matrix as being Bohemian or not, without significant ambiguity.
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