3A.1 Introduction

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Linear algebra, the algebra of sets, vectors, and matrices, is useful in the study of mechanical vibrating

systems in general, and modal analysis in particular. In practical mechanical systems, interactions among

various components are inevitable. There are many response variables associated with many excitations.

It is convenient to consider all excitations (inputs) simultaneously as a single variable, and also all

responses (outputs) as a single variable. Use of linear algebra makes the analysis of such a system

convenient. Modal analysis using such a vector– matrix representation will provide natural frequencies

and mode shapes, as discussed in Chapter 3 and other places in the handbook. The subject of linear

algebra is complex and is based on a rigorous mathematical foundation. In this appendix, we will review

the basics of vectors and matrices.

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