This note is concerned, for matrices with elements in an algebraically closed field of arbitrary characteristic p, with pencils generated by pairs of matrices with property L. A pair of n by n matrices is said to have property L if for a special ordering of the characteristic roots a< of A and Bi of B, the characteristic roots of +ptB are Xa<+p,/3,-for all values of X and pt.(See
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Motzkin et al. (1955) studied this question.