Generalised semi‐tensor product of matrices

Algebraic Relations among Four Types of Right Semi-Tensor Product

“…us, other definitions of right STP, as extensions of linear mappings, are provided. Definition 2 (see [12,17]). Let A ∈ M m×n and x ∈ V r .…”

“…Due to the importance of left MM STP and left MV STP, the authors in [17] explored more general STPs, which help to expand the possible applications of STP. In the following, the left MM STP and left MV STP are denoted by left MM-1 STP and left MV-1 STP.…”

“…By changing the way of dimension expansion, the authors in [17] defined four corresponding right STPs, including right MM-1 STP, right MM-2 STP, right MV-1 STP, and right MV-2 STP. However, relations between these right STPs are not studied.…”

Semi‐tensor product of quaternion matrices and its application

“…Semi-tensor product of matrices proposed by Professor Cheng 1 opens up a new field for us to explore matrix theory, and the various forms of semi-tensor product were defined as Cheng et al 2,3 : matrix-vector semi-tensor product and semi-tensor product of matrices. Semi-tensor product of matrices is widely used in many fields such as biological system, 4,5 game theory, 6,7 graph theory, 8,9 fuzzy control, 10,11 and coding theory.…”