Page 50 - Aeronautical Engineer Data Book

Fundamental dimensions and units 37
Scalar multiplication
A matrix may be multiplied by a number as
follows:
ba ba
a a � � ba ba �
b 11 12 = 11 12
� a a
21 22 21 22
General matrix multiplication
Two matrices can be multiplied together
provided the number of columns in the first
matrix is equal to the number of rows in the
second matrix.
b b
12
11
a a a 13 � ��
12
11
21
� a a a b b 22
21 22 23 b b 32
31
a b +a b +a b a b +a b +a b �
a b +a b +a b
= 11 11 12 22 13 31 11 12 12 22 13 32
� a b +a b +a b
21 11 22 21 23 31 21 12 22 22 23 32
If matrix A is of order (p 2 q) and matrix B is
of order (q 2 r) then if C = AB, the order of C
is (p 2 r).
Transposition of a matrix
When the rows of a matrix are interchanged
with its columns the matrix is said to be trans­
posed. If the original matrix is denoted by A, its
T
transpose is denoted by A' or A .
a a
21
11
a a a � T ��
If A = 11 12 13 then A = a a
� a a a 12 22
21 22 23
a a 23
13
Adjoint of a matrix
] is any matrix and A is the cofactor
If A =[a ij ij
T
the matrix [A ] is called the adjoint of A.
of a ij ij
Thus:
a
a 11 12 ... a 1n A 11 A ... A n1
21
a 21 a 22 ... a 2n A 12 A 22 ... A n2
. . . . . .
A = adj A=
. . . . . .
� . . � � . . . � .
... a
a n1 a n2 mn A 1n A 2n ... A nn