Pairs of Matrices with Property L

Abstract

MOTZKIN AND TA USSK Y D log x = -lx and D log y = -ly have the same meaning, namely, D log = -1>01.Similarly, both D1(12.J3) (x, y) = 2xy3 and D1(I2.J3 (y, x) = 2yx3 stand for D1(I.2J3)= 2*I.J3.Here, the issue is somewhat confused by the traditional reference to J2.J3 as the function x2y3, that is, by its value for (x, y).The connection of the alphabetical order of the variables with the places where they are to be substituted is not germane to the problem. 3The above theory is strikingly analogous to a general theory of mensuration dealing with undefined objects A, B, . . .and numbers such as (B in A).In this theory, (A inand (Cin B) = c, then (C in A) = c b; and measure is multiplicatively contravariant to a change of the unit.