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Kunze Linear Algebra
· Problem 10.1.1
Bilinear Forms
Mathematics — Methods · bilinear-forms-identification
Problem
Which of the following functions
f
f
f
, defined on vectors
α
=
(
x
1
,
x
2
)
\alpha = (x_1, x_2)
α
=
(
x
1
,
x
2
)
and
β
=
(
y
1
,
y
2
)
\beta = (y_1, y_2)
β
=
(
y
1
,
y
2
)
in
R
2
R^2
R
2
, are bilinear forms? (a)
f
(
α
,
β
)
=
1
f(\alpha, \beta) = 1
f
(
α
,
β
)
=
1
. (b)
f
(
α
,
β
)
=
(
x
1
−
y
1
)
2
+
x
2
y
2
f(\alpha, \beta) = (x_1 - y_1)^2 + x_2 y_2
f
(
α
,
β
)
=
(
x
1
−
y
1
)
2
+
x
2
y
2
. (c)
f
(
α
,
β
)
=
(
x
1
+
y
1
)
2
−
(
x
1
−
y
1
)
2
f(\alpha, \beta) = (x_1 + y_1)^2 - (x_1 - y_1)^2
f
(
α
,
β
)
=
(
x
1
+
y
1
)
2
−
(
x
1
−
y
1
)
2
. (d)
f
(
α
,
β
)
=
x
1
y
2
−
x
2
y
1
f(\alpha, \beta) = x_1 y_2 - x_2 y_1
f
(
α
,
β
)
=
x
1
y
2
−
x
2
y
1
.
Related theory
Bilinear Forms
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