Multiplying through by f and integrating shows that......
Then A=B, as one sees by multiplying out the product on the right.
The theory of elementary divisors now shows that by pre- and post-multiplying x by suitable elements of K we can reduce x to a diagonal matrix.
Go to List of words starting with:
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z