Suppose that A is a real symmetric matrix and that A u = λ u , A v = β v , where λ ≠ β , u ≠ θ , and v ≠ θ . Show that u T v = 0 . [ Hint: Consider u T A v .]
Suppose that A is a real symmetric matrix and that A u = λ u , A v = β v , where λ ≠ β , u ≠ θ , and v ≠ θ . Show that u T v = 0 . [ Hint: Consider u T A v .]
Solution Summary: The author shows the equality uTv=0 in a real symmetric matrix.
Suppose that A is a real symmetric matrix and that
A
u
=
λ
u
,
A
v
=
β
v
, where
λ
≠
β
,
u
≠
θ
, and
v
≠
θ
. Show that
u
T
v
=
0
. [Hint: Consider
u
T
A
v
.]
Definition Definition Matrix whose transpose is equal to itself. For a symmetric matrix A, A=AT.
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