设[tex=4.643x1.0]2bOOLS2qYWpFCMCkhOx7kWKBZXCHc0rkmUgF/O9obdwPxSggBAHYEkc4KmIt+owdgvolNqDVZJPv8y6xbkiCkQ==[/tex] 是四维线性空间[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的一组基，已知线性变换[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]在这组基下的矩阵为[tex=9.714x4.786]dEdrC9SQsN/3Vx39SaFo4F4k4j2a4XW0+ki4qRfuccZ3acDq0FvL6o/bF+WQXPHLP+sqGWr3situWKRnWapkr5ed8utdPa1QDBnWmM4vMGRQAeNdtMkTuQmnXcxPCj9/o6UgHc6gwEhnkF/JDVCroXTvP7C5kUQ+7yYTMkDBfGg=[/tex]1） 求[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的核与值域；2） 在[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的核中选一组基，把它扩充成[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的一组基，并求[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]在这组基下的矩阵；3） 在[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的值域中选一组基，把它扩充成[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex] 的一组基，并求[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]在这组基下的矩阵．
解：1）先求[tex=3.0x1.5]3sKL0hlKqRAyih0FQGoD+g==[/tex]．设[tex=4.071x1.5]aCl30G2L0aMGg1wVgMaB1jumYXLVARtpRzcvGhn8CIo=[/tex]，它在[tex=4.643x1.0]2bOOLS2qYWpFCMCkhOx7kWKBZXCHc0rkmUgF/O9obdwPxSggBAHYEkc4KmIt+owdgvolNqDVZJPv8y6xbkiCkQ==[/tex]下的坐标为（[tex=5.071x1.0]f4zu9oWJlcwNIPTwOzLuTVAKjMmJwXJjm9olTDDlwqc=[/tex]），[tex=1.214x1.214]8XA1Vm3y2+zXQOPDku2J2A==[/tex]在[tex=4.643x1.0]2bOOLS2qYWpFCMCkhOx7kWKBZXCHc0rkmUgF/O9obdwPxSggBAHYEkc4KmIt+owdgvolNqDVZJPv8y6xbkiCkQ==[/tex] 下的坐标为[tex=4.143x1.357]ic2NRDP08I8OyHMi+tW0tQ==[/tex]，由文献［１］Ｐ.286 定理３，有[tex=17.5x4.786]dEdrC9SQsN/3Vx39SaFo4F4k4j2a4XW0+ki4qRfuccZ3acDq0FvL6o/bF+WQXPHLP+sqGWr3situWKRnWapkr5ed8utdPa1QDBnWmM4vMGRQAeNdtMkTuQmnXcxPCj9/o6UgHc6gwEhnkF/JDVCroR/fi8v6ye4Gqr72bJpelPz1n+R4qYCpIono+mj9iBsZUsAfHbE/vQs33oBwLq1qEUrBPK7dYDBiSO8pCi0TR+pN4OfVneCJj6uFpBB8/w5vkETq9YzpkyDD5bgUomLFAduZOg4Fer10vPfOW9GqmPFvMPztmhp/GqZtpe/xkURoJnfY489V137y6dl5Tkx9pA==[/tex]因[tex=3.571x1.357]SP6TPMOBNPQYHQzO3UyW/w==[/tex]，只需解前两个方程：[tex=10.857x2.786]fnpmC2J6JmQBLyo5NmGAz5Bo72kJfJcJdFHkIrF1KOrS5gALHSCetTvLBhMAoqM3WvCga4ximOaWclxujCqjS3vUlDnarkW9WS3gQI6Bmcye05DQy8wiaj7ujjIJMkkKUmEToMIJfVXMZDsKwIR92g==[/tex]得基础解系[tex=17.357x1.357]ryOi+Zj9lj+KJ+FYpMkkaXxj7CbMRATTxcuuFSJZ6uDO9oFm+kxvLDQBm9mWiSLFlP+99zrATfO2LPs84Ruiug==[/tex][tex=2.429x1.0]xJr2ny42kcAcTeyzkoXuGtgplTUAoUg88inuy+tLeOI=[/tex] 即为[tex=3.0x1.5]3sKL0hlKqRAyih0FQGoD+g==[/tex]的一组基，所以[tex=7.786x1.5]uJaTKRfIx4i2/C0lnQ3c5kfMSjF0e+prKo3OLAFPZq5XlqIThBZdB9v9xWzlnIIA[/tex]．再求[tex=1.357x1.0]uLg0y0iRi6ORR1JXInrMOQ==[/tex]．由文献［１］Ｐ.303 定理10，有[tex=10.071x1.357]SU8so5lijXOzzZUyT92MuRKv3PudJEHAuVIvmvm007N9MDTlwOg3cP/+zxbVjqtt/cBk0pL0ZYmISZ57RGqht/1HKX28YUpZQ4ND6GgaDDIqe1Hp1vKwuUhu23DMoleIV64CKBwgQgMabBmANcvcRw==[/tex]因为[tex=17.786x1.214]9KIBTVINYLjOvRvWNs7O2BObxEmF0aYvQ+AuxtZ56lgjwnvY8UnDHEjnkhFoI7WoyzvSWuYgoUR2gtndoTNzCtwZ5RJbSsMFhGjBNefDDLuuvFI8KxQOQTGm9UjW0bR5PXPqCgH7qoRJSHcJvA2RbckOy2I22slj1uyDARucv56wZqaGhCcFp9dilqiEPDpi/JOWnWc1fAp2iAaSIHtP/A==[/tex][tex=19.429x1.214]bFFdsdkM8vQq8ynl2taTYOCC0/n0r/K4uk7DtohG3/FhIkMc1/i1skKdLzj6I64YrvptpLKXMbNn6TalU/T4upVHFQbB6uE/roMQahcBa8y0a8OW8rHH/97udIYVNa9C7mkAql+U7teXC0z5+24qMhcoUkgYvKxRRujpwYkB1DeOS41RoDD0gEmEIolWKxd5ks+LNsBfsIBGebz+QoWRadLC1sKB5xSDG0ScLiBuVP4=[/tex]又[tex=7.643x1.214]qwCsUYlaJonXPabr0o+47NndnmRD5Wp6nsrSZ8u7dOmRW/y5uJiQft6U3cg/UiwWgn3BwC445NsFv+/cAnd2wdkEp2LSIFnBGs/GXjDgmFgOAoqBdMHofb5wynsd/dcu6bjxGd0P+OFEMft8fOhuJw==[/tex]的秩为２，且[tex=3.643x1.214]3qkBofe16gEqhoCYCt9w4e9SeF142QZLyc5DUFb3dc34L8Z+lFXWJ07ZAjchPGAY[/tex]线性无关，故组成[tex=1.357x1.0]uLg0y0iRi6ORR1JXInrMOQ==[/tex] 的基， 从而[tex=7.929x1.357]tIN0rq5GhTeB2/uEsmjInuu262bwGs92lXbRTTPq19hISF76oxCzvcj5OmsfMndY04xxVJTUGHCWLYSwS0lUuPHbMqULzVWqeUj5oGjs8zY=[/tex]2)由1）知[tex=2.429x1.0]xJr2ny42kcAcTeyzkoXuGtgplTUAoUg88inuy+tLeOI=[/tex]是[tex=3.0x1.5]3sKL0hlKqRAyih0FQGoD+g==[/tex]的一组基，易知[tex=5.0x1.0]2bOOLS2qYWpFCMCkhOx7kdFeJQ1RK3bn5HUbcuQE5XJwQw1GKr7OjEtZuua8DlN556ZaCO88JJRLxBZXY7JNGA==[/tex] 是[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的一组基，因 为[tex=5.0x1.0]2bOOLS2qYWpFCMCkhOx7kdFeJQ1RK3bn5HUbcuQE5XJwQw1GKr7OjEtZuua8DlN556ZaCO88JJRLxBZXY7JNGA==[/tex][tex=0.786x0.643]NhuTNiqjImitwKaHFutGOg==[/tex][tex=4.643x1.0]2bOOLS2qYWpFCMCkhOx7kWKBZXCHc0rkmUgF/O9obdwPxSggBAHYEkc4KmIt+owdgvolNqDVZJPv8y6xbkiCkQ==[/tex][tex=9.929x5.214]dEdrC9SQsN/3Vx39SaFo4B8usezbIl6DKXEaWVywG/JPIrLzIvfnJv16yT9fsSYRIiQBjzuyZxa+CSLzlQS4iyv9ZSGPF3jBwGENu1q6Mwd6OhgFfzNFaPakiKuLgctaITzaO79uztbb+YfYl9f7mH/GXFbzK/Z8i6LyImOSKsk=[/tex]故[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]在基[tex=5.0x1.0]2bOOLS2qYWpFCMCkhOx7kdFeJQ1RK3bn5HUbcuQE5XJwQw1GKr7OjEtZuua8DlN556ZaCO88JJRLxBZXY7JNGA==[/tex]下的矩阵为[tex=32.429x5.357]GGH5qazUqq7NUCYOcK6l4HKLyD6Q83naKWPRE/hpv5Xt4qXaaD4N1BDQLqyf6jVbPHnyStlx/haGaQdqBoP9WFiIMK+u4tbpmoBZTg/CPFWfB06dplA1AL8z7ujaFV3LoKWt6XT75EbnLlmsFobQCBGLxmrsfNVzJ/6FLLt0cwX9eHv5plyz1yg6jAGcxbKIL/WUu8h7lYYVyFxbYdyNlvVScELTLqtLXkRHQlZTBI0B+9TnnbUhr4cHI0G8R90oeXnXlzCOYjtDrUh2333mAxe4U9PIfLUzsmtzMh+eIx/JBdcvRyAZox7aYojM9/fzeblGmL/6kyyrMPmPlXYe35orBC3Gq7ILD5IpN97DrT8X3nF6ruhfcdLYur8vB3Un9pFaho8FX5HTjmmNq+jT2Jg6i43tr70VcymFjHNcCMAOF/TxIU/Ya3bpkepz6mu/fp4rN0khUBvkXqV5Bl4cF9gOkx2ljuRZLUR5yWeGq7g=[/tex] [tex=29.214x5.214]ThIgXOUyLYK/6IHx89IH/sc2f/Kbs7F0nUTj/Ggk35ZLON/faY2/dbjfjitnW54L+f91GquesLAxlp7nz8jD5Po7zR2LnXIN3vvTp+FU/b2vgdixiCkIenPhLmEYNr7lOV/pOxo/al5PU94vkxnZv1QCroLOb1k//A+xGB/IT53sN/SMyAvcF5EIQ1Z+U/hXTbGhqNibtQ/WoopQAbjrMI95KGrxNpJeLlAAtz+uwHz0T0wkRyXA99Op5VMEXQ2oZSxZOQ4z2P/U0J1WK1BcWHb0vCaZby6DyxeZ5Tezh4aJ5K6v3JPjxsrKBliTWJJxMIg1CML3nx02k8hCS/uurQ+8oKgKmsvYsJNKIiPgeAhnNXmYGEwRHzu9qN24JrJaZXGpntp90vlpzk5uw9NTnm07Aj8PNM3Vj6EJSM7Sw5OuRvMLcT56uHNANZFMnkO83uzuX3uzt64dNqCE6Z8AYg==[/tex] [tex=10.071x5.214]ThIgXOUyLYK/6IHx89IH/pc7OeeyVTj/H4uQtA7pHlHckSozZS5lC7GE+hxTTOhhctIFE6X4MKStKdDwQtq78mHulACA7izbtx/JWX9A5Ss8jCoKRuc2xLr7GgyMzI7nRtgJJgg2r982yRwmEbT3nw2Yjlf8SFKbONNfjoa+sFg=[/tex]3） 由1）知[tex=17.786x1.214]9KIBTVINYLjOvRvWNs7O2BObxEmF0aYvQ+AuxtZ56lgjwnvY8UnDHEjnkhFoI7WoyzvSWuYgoUR2gtndoTNzCtwZ5RJbSsMFhGjBNefDDLuuvFI8KxQOQTGm9UjW0bR5PXPqCgH7qoRJSHcJvA2RbckOy2I22slj1uyDARucv56wZqaGhCcFp9dilqiEPDpi/JOWnWc1fAp2iAaSIHtP/A==[/tex]易知[tex=6.143x1.214]3qkBofe16gEqhoCYCt9w4e9SeF142QZLyc5DUFb3dc11Z/eTxK8VeL9OEFw0fk05mv7Tq2bUVM1sDsfRZX8bXQ==[/tex]是[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的一组基．因为([tex=6.143x1.214]3qkBofe16gEqhoCYCt9w4e9SeF142QZLyc5DUFb3dc11Z/eTxK8VeL9OEFw0fk05mv7Tq2bUVM1sDsfRZX8bXQ==[/tex])[tex=0.786x0.643]NhuTNiqjImitwKaHFutGOg==[/tex][tex=4.643x1.0]2bOOLS2qYWpFCMCkhOx7kWKBZXCHc0rkmUgF/O9obdwPxSggBAHYEkc4KmIt+owdgvolNqDVZJPv8y6xbkiCkQ==[/tex][tex=8.929x4.786]dEdrC9SQsN/3Vx39SaFo4F4k4j2a4XW0+ki4qRfuccagzN6pWRAa1vWeHUCGCIZh5mBaTomr+AsF1x6ljacqsmcIDNuJYqaWSzgto29Qc/IVlvNh/+uUqWyijtp60e/OQ17n1WUrXYDSNKvwj+kwVw==[/tex]故[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]在基[tex=6.143x1.214]3qkBofe16gEqhoCYCt9w4e9SeF142QZLyc5DUFb3dc11Z/eTxK8VeL9OEFw0fk05mv7Tq2bUVM1sDsfRZX8bXQ==[/tex]下的矩阵为[tex=30.429x4.929]hckPS0WZ5y9Dy8+em27JdX2QSj0RnifaFaKpJALSiACIzvEReQ355xwbvhh2KYftAr1DkDnmPf8EPHHlofnn48V0HD16UGbxTQ4Di7Vs0fhkZQRbbdhlZBeARFUvMzIvgV76QD65hcINZp1gNFJMUKfmOPQWpTl9bi0Onb1pgPESJqjp/kQ8NHWfy6n3POddrEfs+BBqNisxJxG2fd4Awb448EsweO5XMf9iOjItGxJy2dWO49D7bH92mF7ApfOVVoQsEpmMMX8FZtwxp4EThGZ/aoczzwXf9SyYo6Nudu8hfzESseue05AbZasGNHfxfRQJyqkJ17r/U1VH8NINoDO7QmQb936dC1JX9rAGQK8VoJZuqmvgudSEfmrlT22Vm+7PKoRPQxfL8EoHLVXtrFbi+4UDovhpSHkMqyIzS9I0mw8u/gz9x1a1ltuq/ZyHqONUmSBNgBAr/mTCB75E1g==[/tex] [tex=29.214x5.214]ThIgXOUyLYK/6IHx89IH/p/e+JKpKamdW8TYqNfrTOcTy2OTOfV2ORNk0szcnKnjPasJieFYPhSPGzUqHCb1AYoPMxLdDdAVUWeXhcy792cE1p3Qeo9pNwr8tYrpMO0Z8qOn/Zcav0HfmykhJKh4p5ts3JcNnJLWAuJksYPYyFKFfHEUvtIaZ5ChReq/+BSlTtcx4FSDgdREJJik5ndwNEqaNvsNUgq2SJh+xYi1kIac7f/mrlri8O7jLWeVBj4hThXPbhpRm4JlI68bmpn7kH23k4A+VqoZEsORnbVIqd66WXivvYA4c9zt4/5PTvY0k+tlluO+GSpzWUtq8ZyfYt+ijDMC9gFQxN2aHTRIqOrXeyJmTBAHajKOKfwK44rInwC62MeqVt0F/17LrER2CfrHNvNmqABHebD2I/y3qUU3s67GNPHV21SYUiXU9xI321zR5EaQ4UBVjThpdstgLQ==[/tex] [tex=10.286x5.214]ThIgXOUyLYK/6IHx89IH/pc7OeeyVTj/H4uQtA7pHlF7npJ0bqSbHgbksm1Ht5DB3huGcIjnoYzDXUIoSgecMlhLOJHdE65yj69yfOdO4WWm9DLYPknY3olACWEPmEjT4XfEQOv60vNbNJRzjVSomhcxe1B60FEvSb+NimQdElc=[/tex]
举一反三
- 求解下列矩阵对策,其中赢得矩阵 [tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex] 为$\left[\begin{array}{llll}2 & 7 & 2 & 1 \\ 2 & 2 & 3 & 4 \\ 3 & 5 & 4 & 4 \\ 2 & 3 & 1 & 6\end{array}\right]$
- 求复数域上线性变换空间[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex] 的线性变换[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex] 的特征值与特征向量.已知[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]在一组基下的矩阵为:[tex=6.214x2.786]sSXBpxJWudVpH1R35o4LnICFRL28yBYsK66HeilXyE6CC47hOP02bOALCujE3jwKBlrph0855TMfIxwneXt19w==[/tex]
- set1 = {x for x in range(10)} print(set1) 以上代码的运行结果为？ A: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} C: {1, 2, 3, 4, 5, 6, 7, 8, 9} D: {1, 2, 3, 4, 5, 6, 7, 8, 9,10}
- [tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]是[tex=0.643x0.786]SBMIs+VUk7//BOpfqlQl0w==[/tex]级线性空间[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]上的线性变换． １） 若[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]在[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的某组基下矩阵[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]是某多项式[tex=1.929x1.357]EJ5ekqmr2bWoAT+xH4aA4Q==[/tex]的伴侣阵，则[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的最 小多项式是[tex=1.929x1.357]EJ5ekqmr2bWoAT+xH4aA4Q==[/tex]． ２） 设[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的最高次的不变因子是[tex=1.929x1.357]EJ5ekqmr2bWoAT+xH4aA4Q==[/tex]，则[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的最小多项式是[tex=1.929x1.357]EJ5ekqmr2bWoAT+xH4aA4Q==[/tex]．
- 求复数域上线性空间[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的线性变换[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的特征值与特征向量，已知[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]在一组基下的矩阵为[tex=5.786x2.786]hB8sGfF8hpZRTKdvt1J/eID9fNghG5RBsDIPY/vVGtTza7ol+NMStiGlU9bmYU1HsjInbJ0o9Jl5CxUyUwoXog==[/tex]
内容
- 0
求复数域上线性变换空间[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的线性变换[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex] 的特征值与特征向量.已知 [tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex] 在一组基下的矩阵为:[tex=9.5x3.929]sSXBpxJWudVpH1R35o4LnIcNXurDIqYZ4dH4l1OxViDlMo63aWtGmjOJfggNcg2J+Vks/cV38rcVeic5yfu+bGXmD4F++M6K2iUBT1zCdlcHcA4BtkekP2I/wslns5W3[/tex]
- 1
设 [tex=4.643x1.0]A4jSygN0882R6SV3eve5dyhKA/5f6aU7CkpCJuZGXtlw94feNCK40XN+rRjedTwKiT6M+7G+X0+NO323Q0MGX66zshUAJc1cAnQFN9WrDFU=[/tex] 是四维线性空间 [tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex] 的一组基,已知线性变 换[tex=0.857x1.0]xs/zPwdLSSAmQIIfXPkuWQ==[/tex] 在这组基下的矩阵为[tex=10.143x4.786]075gCzZzsMRb6HYXYk9X96ka3vrvpAflUM3U1ay2rhWeMSYxbzIA6i9pHOj+/jMgJ+B+LdRkrccbbNQF/J6EGVKcWj49gntQBbYc8e82Dzet9XQOVHfr2JFiMdTaNdYKC6AOvj05/eFigNzVPIzpVVvcd34oo5JxpLTixSWCM3A=[/tex]再[tex=0.857x1.0]xs/zPwdLSSAmQIIfXPkuWQ==[/tex]的核中选一组基,把它扩充成 [tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]的一组基,并求[tex=0.857x1.0]xs/zPwdLSSAmQIIfXPkuWQ==[/tex]在这组基下的矩阵
- 2
>>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']
- 3
设[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]是线性空间[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]上的可逆线性变换．证明：１） [tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的特征值一定不为０；２） 如果[tex=0.643x1.0]7dwHQGHL24uGORI8NryViw==[/tex]是[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的特征值，那么[tex=1.643x1.357]7hXLKuNcz29qRRA2zjn4rA==[/tex]是[tex=1.714x1.214]d+9NDUvA5ZDrRGeFW5fxcQ==[/tex]的特征值．
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采用基2时间抽取FFT算法流图计算8点序列的DFT，第一级的数据顺序为 A: x[0],x[2],x[4],x[6],x[1],x[3],x[5],x[7] B: x[0],x[1],x[2],x[3],x[4],x[5],x[6],x[7] C: x[0],x[4],x[2],x[6],x[1],x[5],x[3],x[7] D: x[0],x[2],x[1],x[3],x[4],x[6],x[5],x[7]