MAGIC MOORE-PENROSE INVERSES AND PHILATELIC MAGIC SQUARES WITH SPECIAL EMPHASIS ON THE DANIELS–ZLOBEC MAGIC SQUARE

Abstract

We study singular magic matrices in which the numbers in the rows and columns and in the two main diagonals all add up to the same sum. Our interest focuses on such magic matrices for which the Moore–Penrose inverse is also magic. Special attention is given to the “Daniels–Zlobec magic square’’ introduced by the British magician and television performer Paul Daniels (b. 1938) and considered by Zlobec (2001); see also Murray (1989, pp. 30–32). We introduce the concept of a “philatelic magic square” as a square arrangement of images of postage stamps so that the associated nominal values form a magic square. Three philatelic magic squares with stamps especially chosen for Sanjo Zlobec are presented in celebration of his 70th birthday; most helpful in identifying these stamps was an Excel checklist by Männikkö (2009).

Keywords

• magic matrix
• Moore–Penrose inverse
• Paul Daniels
• philatelic magic square