设 [tex=1.786x1.214]s/df2ZE+BhF7kkKI1Rb3ww==[/tex] 为 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶正交矩阵, 证明: [tex=4.714x1.357]AehmnmndNC1Hrl0sLgD82w==[/tex] 当且仅当 [tex=4.929x1.357]bImpolCTp68FxhYHaH6V5G+EvEyE/7E9eP0IUefSyZc=[/tex] 为奇数.
举一反三
- 设[tex=1.786x1.214]s/df2ZE+BhF7kkKI1Rb3ww==[/tex]为[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]阶正交矩阵,且[tex=4.0x1.357]POsnup5weJxpS5OVpIh35VHXUbKJ/mqqbwb4d3G7lj4=[/tex],证明[tex=2.286x1.143]2zmmF6+x7+n6wGG+8KOAbQ==[/tex]为不可逆矩阵.
- 设 [tex=1.786x1.214]s/df2ZE+BhF7kkKI1Rb3ww==[/tex] 都是 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶矩阵, [tex=1.786x1.214]s/df2ZE+BhF7kkKI1Rb3ww==[/tex] 有相同的特征值, 且这 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 个特征值互不相等. 求证: 存在 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶矩阵 [tex=1.714x1.214]+50NLKmQlExnsgtF9o5osQ==[/tex], 使 [tex=6.714x1.214]iWx5GMtLVkHKqZmcNE8Au/1+cNI14CBoocJqKqvHS60=[/tex]
- 设[tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex]为[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶正交矩阵，且 [tex=4.929x1.357]MzmmROCjjtWxSw9nY2Sa7JDHd0yCD0R+oQfEalFNnpqw+tbmoDzJsgbxLqaHKrro[/tex], 证明 [tex=5.214x1.357]pO4mVdCTes08WUz+JKp3fRf3OB7iWXYe/WEWOxALuI3jRpCcG75exFCbkTaNpxhx[/tex]
- 设 [tex=0.714x1.0]YiLkHgl7MlxE+QjUplQUKA==[/tex] 是 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶矩阵, 求证: 存在 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶矩阵 [tex=1.786x1.214]s/df2ZE+BhF7kkKI1Rb3ww==[/tex], 使 [tex=5.357x1.143]Wbhpk6fsBNi2qM8u+WL7eg==[/tex]的充要条件是 [tex=3.286x1.0]ApBtKiFHAOgbksEzlkUgQcH0xASBEp8gGImmCF1jAes=[/tex]
- 设 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 阶方阵[tex=1.786x1.214]s/df2ZE+BhF7kkKI1Rb3ww==[/tex] 满足: [tex=16.0x1.5]wBEIG6guqialGrZHLnnVUrWGvcifjiMu86GbQoXU/LU1jrnjwVhijVnC+EaC2FGdkdlep1rF96g79s4AkIF1FQ==[/tex], 证明:[tex=11.5x1.429]73j1TLguTjvjYIO320L0CT4CvEv7s3is45tNUqTDfRMOiHOk9vb4ONFWmSVuG3BM[/tex]