Inner Products, Projections and the SVD · 免费预览

内积

内积

1. Inner Products

Inner Products

2. Quick check: Bilinearity of the inner product

For vectors x,y,zx, y, z and scalars λ\lambda, which identity holds for an inner product?

3. Dot product of orthogonal vectors

If x,y∈Rnx, y \in \mathbb{R}^n are orthogonal then ⟨x,y⟩=\langle x, y\rangle = ______ .

4. Symmetry of the inner product

For a real inner product, which axiom relates ⟨x,y⟩\langle x, y\rangle and ⟨y,x⟩\langle y, x\rangle?

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