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Kunze Linear Algebra
· Problem 10.2.3
Bilinear Forms
Mathematics — Methods · non-degenerate-quadratic-form-r2
Problem
Let
q
(
x
1
,
x
2
)
=
a
x
1
2
+
b
x
1
x
2
+
c
x
2
2
q(x_1, x_2) = ax_1^2 + bx_1 x_2 + cx_2^2
q
(
x
1
,
x
2
)
=
a
x
1
2
+
b
x
1
x
2
+
c
x
2
2
be the quadratic form associated with a symmetric bilinear form
f
f
f
on
R
2
R^2
R
2
. Show that
f
f
f
is non-degenerate if and only if
b
2
−
4
a
c
≠
0
b^2 - 4ac \neq 0
b
2
−
4
a
c
=
0
.
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