Matrix Multiplication, the Inverse Matrix and Partitioning

Abstract

Matrix multiplication is based on the product ab of an n element row vector a = [a ₁, a ₂, a _n ] and an n element column vector b = [b ₁, b ₂, b _n ]^T. This product of vectors written ab, and called the inner product or scalar product of the matrix row vector a and the matrix column vector b, is defined as

$$ {\mathbf{ab}} = {a_1}{b_1} + {a_2}{b_2} + \cdots + {a_n}{b_n} = \sum\limits_{i = 1}^n {{a_i}} {b_i} $$

(3.1)