Matrix-vector multiplication is fundamentally defined as forming a linear combination of the columns of the matrix, where the entries of the vector serve as the coefficients weighting each column — this reframing (rather than the row-by-row dot-product view) is presented as the foundational operation of linear algebra. Matrices themselves are understood as rectangular arrays representing structured data or relational systems (e.g., networks, where entries encode connections between nodes), making linear combination the core mechanism by which linear algebra models and manipulates such data. This concept belongs to introductory linear algebra and underlies the broader discipline's treatment of vector spaces, span, and linear transformations.
Matrix-vector multiplication is fundamentally defined as forming a linear combination of the columns of the matrix, where the entries of the vector serve as the coefficients weighting each column — t…