黄克智版张量分析习题解析
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1.1 求证:u×(v×w)=(u·w)v-(u·v) w 并问: u×(v×w) 与 (u×v)×w 是否相等?u,v,w 为矢量。
证明:
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v w vx vy vz wx wy wz
vywz vzwy i vzwx vxwz j vxwy vywx k
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u v w ux
1.3 求证矢量的非退化性。即:若矢量 v 与它所属的矢量空间 中的任意矢量 u 都正交,即:u·v=0,则矢量 v=0。
证明:因为 u 为任意,所以可取 u1,u2,u3,使得
u1x u1y u1z det U u2x u2 y u2z 0
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1.2 求证: (A×B) ×(C×D)=B(A·C×D) -A(B·C×D) =C(A·B×D) -D(A·B×C)
证明:
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