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证明: 设 α=(a1,a2,...,an)^T, β=(b1,b2,...,bn)^T则 β^Tα=α^Tβ=a1b1+a2b2+...+anbn--这是向量的内积而 αβ^T =a1b1 a1b2 ... a1bna2b1 a2b2 ... a2bn ... ...anb1 anb2 ... anbn所以 tr(αβ^T)=a1b1+a2b2+...+anbn=β^Tα.同理可证 tr(βα^T)=a1b1+a2b2+...+anbn=β^Tα.所以有 tr(αβ^T)=tr(βα^T)=β^Tα=α^Tβ.... |
