## Appendix A

### Review of Matrix Algebra and Matrix Calculus

##### A.1 REVIEW OF MATRIX ALGEBRA

Finite element method can be viewed as a means of forming matrix equation that approximates behaviour of a physical system. Hence, any finite element application results in forming, manipulating and solving matrix equations. Therefore, matrix algebra pertaining to finite element analysis is reviewed here.

#### A.1.1 Definition of a Matrix

A matrix is an *m* × *n* array of numbers arranged in *m* rows and *n* columns.

Size of [*a*] = *m* × *n*

*a*_{ij}→element of [*a*] corresponding to *i* th row and *j* th column.

#### A.1.2 Types of Matrices

1. Column matrix (vector) – *n =* 1: