关于E^n中p维与q维超平面间的距离

On distance between pdimensional and qdimensional planes in En

设Ｅｎ中ｐ维与ｑ维超平面分别为πｐ：α１∧α２∧…∧αｐ∧（ｘ－ｘ０）＝０，πｑ：β１∧β２∧…∧βｑ∧（ｙ－ｙ０）＝０，｛γ１，γ２，…，γｔ｝是向量组｛α１，α２，…，αｐ，β１，β２，…，βｑ｝的一个极大线性无关组，则πｐ与πｑ间的距离平方为：ｄ２（πｐ，πｑ）＝｜δ０｜２－γ１δ０，…，γｔδ０［］γｉγｊ［］－１γ１δ０，…，γｔδ０［］Ｔ其中δ０＝ｘ０－ｙ０．

et pdimensional and qdimensional planes in En are respectively.πp: α1∧α2∧…∧αp∧(x-x0)=0, πq: β1∧β2∧…∧βq∧(y-y0)=0. {γ1, γ2, …, γt} is maximal linearly independent subset of {α1, α2, …, αp, β1, β2, …, βq}. Then the square of distance between plane πp and plane πq isd2(πp, πq)=|δ0|2-γ1δ0, …, γtδ0γiγj-1γ1δ0, …, γtδ0TWhere δ0=x0-y0.