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Orthogonal projection
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Area of mathematics
Analysis
Functional analysis
Hilbert space
Closest point theorem in a Hilbert space
Orthogonal decomposition by a closed subspace
Created
2026-09-24
Updated
2026-09-24
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The
orthogonal projection
P
F
onto
a
closed subspace
F
sends
x
to the component in the decomposition
x
=
P
F
x
+
(
I
−
P
F
)
x
with
(
I
−
P
F
)
x
∈
F
⊥
. It is
a
contraction:
∥
P
F
x
∥
≤
∥
x
∥
.
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Orthogonal decomposition by a closed subspace
Closest point theorem in a Hilbert space
Hilbert space
Functional analysis
Analysis
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2025
/
iii
/
Paper 106
/
3
/
a
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 359
/
1
/
b
/
i
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 359
/
2
/
a
/
i
/
Solution
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