Page 26 - Computational Colour Science Using MATLAB

2

Linear Algebra for Beginners

2.1 Some basic definitions
A matrix is a rectangular array of numbers and the numbers in the array are
called the entries in the matrix. A two-dimensional matrix with one dimension
equal to 1 is sometimes called a row matrix (a matrix with only one row) or a
column matrix (a matrix with only one column). A matrix with both dimensions
equal to 1 is simply a single number which we can also call a scalar. It is
conventional to denote matrices by boldface upper-case symbols and row or
column vectors by lower-case symbols. So, for example, the matrix A, where

1 0
0 1
A ¼
is a 2 2 matrix with four entries. Since only the diagonal entries (from top left to
bottom right) are non-zero we can state that A is a diagonal matrix (furthermore,
a diagonal matrix whose diagonal entries are all 1 is also called an identity
matrix).
Two matrices are defined to be equal if they have the same size and their
corresponding entries are equal. If A and B are matrices of the same size, then the
sum A+B is the matrix obtained by adding the entries of B to the corresponding
entries of A, and the difference A B is the matrix obtained by subtracting the
entries of B from the corresponding entries of A. Only matrices of the same size
can be added or subtracted. As an example, if we defined the matrix B by

1 2
,
3 4
B ¼
then we can write that

2 2
3 5
A þ B ¼
and that

Computational Colour Science Using MATLAB. By Stephen Westland and Caterina Ripamonti.
& 2004 John Wiley & Sons, Ltd: ISBN 0 470 84562 7