Linear Algebra Done Right · Problem 6C.15

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · minimization-problems

Problem

In R4\mathbf{R}^4, let U=span⁡((1,1,0,0),(1,1,1,2)).U = \operatorname{span}((1, 1, 0, 0), (1, 1, 1, 2)). Find u∈Uu \in U such that ∥u−(1,2,3,4)∥\|u - (1, 2, 3, 4)\| is as small as possible.

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