VECTOR/MATRIX ALGEBRA

As has already been remarked, this book is written largely in the language of matrix algebra. Since this subject is now so well covered in undergraduate mathematics courses and in numerous text books, (2.1, 2.11) we make only a few observations here.

In this treatment no formal distinction is made between vectors and matrices, the former being simply column matrices. In particular the familiar vectors of mechanics, such as force and velocity, are simply three – element column matrices. For the most part we use boldface capital letters for matrices, e. g. A = [aw], and boldface lower case for vectors, e. g. v = [vi. The transpose and inverse are denoted by superscripts, e. g. AT, A-1. The scalar product then appears as

U • V = UTV

and the vector product as

u x v — uv

where u is a skew-symmetric 3×3 matrix derived from the vector u, i. e.

As usual the identity matrix is denoted by

I = [*„]

in which is the Kronecker delta.