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## Introduction

Welcome to LibMIA.

LibMIA is a software library designed to make manipulation of multi-indexed arrays (MIAs) easy. Technical computing packages, such as MATLAB, GNU Octave, and SciPy, support matrix algebra, making code look remarkably similar to what a scientist or practitioner would write on paper. However, matrices are not well-suited to work with and operate on MIAs, such as those found in digital imagery. What's needed is a formalism and supporting software designed for MIAs.

## MIA Formalism

If you're familiar with Einstein notation, then you already know much of MIA formalism. Nonetheless, there are important differences.

An inner product, $c$, between two arrays $a_{i}$ and $b_{i}$, each of dimension $n$, is the summation of the products of all corresponding elements:

$ c=\sum_{i=1}^{n}a_{i}b_{i} $