Vol. 37, No. 1, 1971

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Triangular matrices with the isoclinal property

Leroy John Derr

Vol. 37 (1971), No. 1, 41–43

Consider the system V n of n × n, lower triangular matrices over the real numbers with the usual operations of addition, multiplication and scalar multiplication and with the additional property that ai+1,j+1 = ai,j (isoclinal). It is shown that V n is a commutative vector algebra. The principal theorem (§3) establishes the existence of an algebraic mapping of V n into a ring of rational functions. This mapping associates a special set of basis elements in V n with the classically known Eulerian Polynomials.

Mathematical Subject Classification 2000
Primary: 15A30
Received: 22 July 1970
Published: 1 April 1971
Leroy John Derr