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Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 326
/
4
/
2
/
c
/
Solution
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2021
iii
Paper 326
4
2
c
2026-09-29
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The supports of
φ
1
and
φ
2
are disjoint, so they are
orthogonal vectors
. Substitution in the
covariance
formula
gives
C
φ
1
=
2
1
∥
φ
1
∥
2
φ
1
=
2
λ
1
(
A
)
φ
1
,
(1)
and
C
φ
2
=
2
1
∥
φ
2
∥
2
φ
2
=
2
1
−
λ
1
(
A
)
φ
2
.
(2)
Therefore the associated
eigenvalues
are
γ
1
=
2
λ
1
(
A
)
,
γ
2
=
2
1
−
λ
1
(
A
)
.
(3)
Ancestors
(12)
c
2
4
Paper 326
iii
2021
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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