Page 49 - Aeronautical Engineer Data Book

36 Aeronautical Engineer’s Data Book
Square matrix
This is a matrix having the same number of
rows and columns.
� 11 a 12 a 13 �
a
23 is a square matrix of order 3 2
a
a
a
22
21
a 31 a 32 a 33 3.
Diagonal matrix
This is a square matrix in which all the elements
are zero except those in the leading diagonal.
� a 11 0 0 �
0 is a diagonal matrix of order 3
0 a 22
0 0 a 33 2 3.
Unit matrix
This is a diagonal matrix with the elements in
the leading diagonal all equal to 1. All other
elements are 0. The unit matrix is denoted
by I.
��
1 0 0
I = 0 1 0
0 0 1

Addition of matrices
Two matrices may be added provided that they
are of the same order. This is done by adding
the corresponding elements in each matrix.

a a a 13 � � b b b �
b b b
13
12
11
11
12
� a a a +
21 22 23 21 22 23
a + b
a + b a + b a + b �
= 11 11 12 12 13 13
� a + b a + b
21 21 22 22 23 23
Subtraction of matrices
Subtraction is done in a similar way to addition
except that the corresponding elements are
subtracted.
a a 12 – b b 12 = a – b a –b 12 �
11
12
11
11
11
� a 21 a 22 � � b 21 b 22 � � a 21 –b 21 a 22 –b 22