The Twelve Triangular Matrix Forms of the Pascal Triangle: a Systematic Approach with the Set of Circulant Operators

This work is devoted to a systematic investigation of triangular matrix forms of the Pascal Triangle. To start, the twelve matrix forms (collectively referred to as G-matrices) are presented. To highlight one way in which the G-matrices relate to each other, a set of four operators named circulant operators is introduced. These operators provide a new insight into the structure of the space of square matrices. Key–Words: Pascal Matrices, Pascal Triangle, Circulant Operators, Square Matrix bipartition, cobweb Partition, G-matrices,