A family of face products of matrices and its properties
The author discusses the usefulness of new types of matrix operations. Let \(A=[a_{ij}]\) be a \(p\times q\) matrix. If \(B_i\) denotes row \(i\) of the \(p\times s\) matrix \(B\) and \(C_j\) denotes column \(j\) of the \(r\times q\) matrix \(C\), then the face product of \(A\) and \(B\) is the \(p\times qs\) matrix \[ A\square B=[a_{ij}B_i], \] and the transposed face product of \(A\) and \(C\) is the \(pr\times q\) matrix \[ A\bullet C=[a_{ij}C_j]. \] Results are obtained involving these operations and the usual operations of sum, product, Hadamard product, and Kronecker product.
scientific article; zbMATH DE number 1439541
scientific article