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16.-Linear-Algebra-by-Kenneth-Hoffman
· Problem 10.3.11
Bilinear Forms
Mathematics — Linear Algebra · skew-form-r3-functionals
Problem
Let
f
f
f
be any skew-symmetric bilinear form on
R
3
R^3
R
3
. Prove that there are linear functionals
L
1
L_1
L
1
,
L
2
L_2
L
2
such that
f
(
α
,
β
)
=
L
1
(
α
)
L
2
(
β
)
−
L
1
(
β
)
L
2
(
α
)
.
f(\alpha, \beta) = L_1(\alpha) L_2(\beta) - L_1(\beta) L_2(\alpha).
f
(
α
,
β
)
=
L
1
(
α
)
L
2
(
β
)
−
L
1
(
β
)
L
2
(
α
)
.
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