Pythagorean theorem in an inner-product space

If

u

and

v

are orthogonal, then

∥ u + v ∥^{2} = ∥ u ∥^{2} + ∥ v ∥^{2} .

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Canonical gradient
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Past exam of the mathematics course of the University of Cambridge / 2004 / ib / Paper 4 / 1E / Solution
Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 39 / 6 / c / Solution
Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 36 / 2 / d / Solution
Past exam of the mathematics course of the University of Cambridge / 2020 / ib / Paper 2 / 18H / a / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 4 / 6B / a / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 4 / 6B / b / Solution
Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 318 / 5 / 1 / a / Solution
Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 318 / 5 / 2 / c / Solution
Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 201 / 3 / b / Solution
Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 205 / 3 / Solution

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