The Moore-Penrose Inverse in Art

Dirk Huylebrouck
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013)
Pages 377–382 Regular Papers


The “Moore-Penrose inverse” of a matrix A corresponds to the (unique) matrix solution X of the system AXA=A, XAX=X, (AX)T=AX, (XA)T=XA. This generalized inverse has many applications, ranging from Gauss’ historical prediction for finding Ceres to modern electrical engineering problems. The present paper provides some applications related to art: one about mathematical color theory, and one about curve fitting in architectural drawings or paintings.