Matrix multiplication is defined within linear algebra as a computational mechanism representing the composition of sequential linear transformations applied to vector spaces. Formally, the product of two matrices corresponds to applying the transformation associated with the right-hand matrix followed by that of the left-hand matrix, where the columns represent the images of basis vectors under this composite mapping. This structural definition establishes non-commutativity as a fundamental property while ensuring associativity through the inherent grouping of sequential functional applications.
Prerequisite chain context: requires Cross Product Area and Direction in Linear Algebra using Right-Hand Rule.