# MoA Interpretation of the Iterative Conjugate Gradient Method with Psi Reduction - A Tutorial to teach the Mathematically literate in Linear and Tensor Algebra: Part I

## TL;DR

This tutorial explains the MoA interpretation of the iterative conjugate gradient method with Psi reduction, aiming to aid mathematically literate individuals in understanding advanced linear and tensor algebra concepts for applications in AI, HPC, and more.

## Contribution

It provides a clear, evolving tutorial on MoA and Psi calculus, connecting foundational mathematics to practical computational methods and design verification.

## Key findings

- Enhanced understanding of MoA interpretation for conjugate gradient methods
- Clarification of Psi calculus applications in tensor algebra and algorithm design
- Facilitation of learning for mathematically literate audiences in advanced linear algebra

## Abstract

It is often difficult to learn new mathematics semantically and syntactically, even when there are similarities in the words and meaning when discussed aloud. The goal of this document is to facilitate learning through explanations and definitions relating our common mathematical knowledge and highlighting what is new. It is meant to be a working document that will evolve based on feedback from target audiences, those mathematically literate in linear and tensor algebra, those that want to learn MoA, Psi Calculus, and its uses, those that want and need the ability to prove a design, either in hardware or software through the ONF, Operational Normal Form, and those wanting to exploit all resources optimally, especially when Tensor Algebra, i.e. algorithms foundational to their application,are needed: Knowledge Representation, Machine Learning, Signal Processing, AI, HPC, etc.