Linear Algebra and Its Applications · Problem 3.1.40

Orthogonality — Gilbert Strang

Mathematics · orthogonal-subspaces

Problem

Suppose LL is a one-dimensional subspace (a line) in R3\mathbf{R}^3. Its orthogonal complement L⊥L^\perp is the \_\_\_\_ perpendicular to LL. Then (L⊥)⊥(L^\perp)^\perp is a \_\_\_\_ perpendicular to L⊥L^\perp. In fact (L⊥)⊥(L^\perp)^\perp is the same as \_\_\_\_.

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