This concept defines the linear algebraic operation where a matrix acts upon a column vector through row-by-column summation governed by the distributive properties of scalar multiplication and addition, formally constituting a specific instance of elemental dot products extended across high-dimensional spaces. It establishes that the resulting transformation maps vectors from an n-dimensional domain to an m-dimensional codomain based strictly on the conformability constraints where the inner dimensions match. This mechanism serves as the fundamental computational rule within linear systems theory for representing linear transformations without explicit matrix-matrix multiplication or iterative decomposition, distinguishing it from element-wise broadcasting operations found in parallel computing architectures.
Computes a matrix-vector product by taking the dot product of each matrix row with the column vector.