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For column vectors x,y∈Rnx, y \in \mathbb{R}^nx,y∈Rn, what are x⊤yx^\top yx⊤y and xy⊤xy^\topxy⊤ respectively?
Both x⊤yx^\top yx⊤y and xy⊤xy^\topxy⊤ are n×nn \times nn×n matrices
x⊤yx^\top yx⊤y is a scalar; xy⊤xy^\topxy⊤ is an n×nn \times nn×n matrix (the outer product)
x⊤yx^\top yx⊤y is an n×nn \times nn×n matrix; xy⊤xy^\topxy⊤ is a scalar
Both x⊤yx^\top yx⊤y and xy⊤xy^\topxy⊤ are scalars
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