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Miklós Schweitzer
1961 Miklós Schweitzer
5
5
Part of
1961 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1961- Problem 5
Source:
11/22/2015
5. Determine the functions
G
G
G
defined on the set of all non-zero real numbers the values of which are regular matrices of order
2
2
2
, and the functions
f
f
f
mapping the two-dimensional real vector space
E
2
E_2
E
2
into itself, such that for any vector
y
∈
E
2
y \in E_2
y
∈
E
2
and for any regular matrix
X
X
X
of order
2
2
2
,
f
(
X
y
)
=
G
(
d
e
t
X
)
X
f
(
y
)
f(X_y)= G(det X)Xf(y)
f
(
X
y
)
=
G
(
d
e
tX
)
X
f
(
y
)
(
d
e
t
X
det X
d
e
tX
denotes the determinant of
X
X
X
).(A. 5)
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