CS223 · Annotated SlidesChapter 6 — Orthogonal Sets and Orthogonal Matrices
Chapter 6 · Annotated slides

Orthogonal Sets and Orthogonal Matrices

Orthogonal and orthonormal sets and bases, weights in an orthogonal basis cⱼ = (y · uⱼ)/(uⱼ · uⱼ), and matrices with orthonormal columns (UᵀU = I).

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  1. An orthogonal set of nonzero vectors is linearly independent. In an orthogonal basis, y = Σ cⱼuⱼ with cⱼ = (y · uⱼ)/(uⱼ · uⱼ): no row reduction needed.

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      Slide 4: Orthogonal Matrix
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      1. Orthonormal columns ⇔ UᵀU = I. A square such U is an orthogonal matrix: U⁻¹ = Uᵀ, and it preserves lengths and angles.
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      MCQ

      For an orthogonal (square) matrix U, U⁻¹ equals:

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