@article{PalanthandalamMadapusi2007WhatAT,
title={What Are the Physical Dimensions of the A Matrix?},
author={Harish J. Palanthandalam-Madapusi and Dennis S. Bernstein and Ravinder Venugopal},
journal={2007 American Control Conference},
year={2007},
pages={2491-2496}
}

Physical dimensions are the link between mathematical models and the real world. In this article we extended results of the work of Hart (1995) by determining the dimensional structure of a matrix under which standard operations involving the inverse, powers, exponential, and eigenvalues are valid. These results were applied to state space models. We also distinguished between different types of dimensionless units.

This chapter discusses singular perturbation theory applied to a problem in biochemical kinetics, and three techniques applied to the simple pendulum.Expand

Dimension analysis is promoted as a technique that promotes better understanding of the role of units and dimensions in mathematical modelling problems. The authors' student base consists of… Expand

0. Introductory.- 0.1 Physical Dimensions.- 0.2 Mathematical Dimensions.- 0.3 Overview.- Exercises.- 1. The Mathematical Foundations of Science and Engineering.- 1.1 The Inadequacy of Real Numbers.-… Expand

This chapter discusses the development of models for Dimensionless Variables based on the models developed in the book “Dimensional Modeling: Foundations of Dimensional Systems” by Pal Rozsa.Expand