设 [tex=7.143x1.429]AWbQ/81wF3sYHzx+DT7PnoAmoOQkxeEh327kZd7V08HG4wz8rURWiUlZRzPWXCQN[/tex] 证明：1) [tex=13.929x4.786]onCAVcUWVxmCLpulhPqtUmnDcqZXcDBpuBjCthxufPNsD9tNShayA2YZJe0hmSMuHWdW5xPQ05HGGJDzi0/vUXOh0Yun+aqpl/rKngYv8p8IAvgGFTK+8pspPrKjRwdzbSdXFClvEIC9jqoh6N2wWFRMcfowSwzOWDzHkLy7q+Y=[/tex]2) [tex=2.5x1.071]+9sd31AjP+sauwAW4OSAZw==[/tex] 时，有 [tex=6.929x1.5]ifzhwOwU8xKM8WoMy+g9tOPou7COcMwFyBCOo2XkyEOBvsMqIjSUdmDLcSRatjug[/tex]
设 [tex=7.143x1.429]AWbQ/81wF3sYHzx+DT7PnoAmoOQkxeEh327kZd7V08HG4wz8rURWiUlZRzPWXCQN[/tex] 证明：1) [tex=13.929x4.786]onCAVcUWVxmCLpulhPqtUmnDcqZXcDBpuBjCthxufPNsD9tNShayA2YZJe0hmSMuHWdW5xPQ05HGGJDzi0/vUXOh0Yun+aqpl/rKngYv8p8IAvgGFTK+8pspPrKjRwdzbSdXFClvEIC9jqoh6N2wWFRMcfowSwzOWDzHkLy7q+Y=[/tex]2) [tex=2.5x1.071]+9sd31AjP+sauwAW4OSAZw==[/tex] 时，有 [tex=6.929x1.5]ifzhwOwU8xKM8WoMy+g9tOPou7COcMwFyBCOo2XkyEOBvsMqIjSUdmDLcSRatjug[/tex]
设 [tex=16.143x1.357]AWbQ/81wF3sYHzx+DT7PniQi2IM7iNBspjrne1469K2GHu9VEC2DYzqKYZXoLiYwmIGvratvKsfhq90ObVceO9RFWJzQ06o3GGEZXNFFzwJadSJP+eO+R+WzehzUoevex/9qUjJpv9PmQ+M96AoPmA==[/tex]，又 [tex=0.786x1.0]O9mrDPbtU/j67mXVbT2dlg==[/tex] 可逆. 证明[p=align:center][tex=14.929x2.786]EBRjOWcqgfP05EAD3oytK0EEoPslrOMvwHfwFPu4wzFcOmAMroeoXBWqOqPdRoejDywlNeXF5Oh3nSDZlbyd9OCI2qJU0/aPXVjatCmnGPKtPuyZmhjG5b5VsJdcMWnd2d/SI+RcYumI1PK8zBYqNQ==[/tex].[br][/br]
设 [tex=16.143x1.357]AWbQ/81wF3sYHzx+DT7PniQi2IM7iNBspjrne1469K2GHu9VEC2DYzqKYZXoLiYwmIGvratvKsfhq90ObVceO9RFWJzQ06o3GGEZXNFFzwJadSJP+eO+R+WzehzUoevex/9qUjJpv9PmQ+M96AoPmA==[/tex]，又 [tex=0.786x1.0]O9mrDPbtU/j67mXVbT2dlg==[/tex] 可逆. 证明[p=align:center][tex=14.929x2.786]EBRjOWcqgfP05EAD3oytK0EEoPslrOMvwHfwFPu4wzFcOmAMroeoXBWqOqPdRoejDywlNeXF5Oh3nSDZlbyd9OCI2qJU0/aPXVjatCmnGPKtPuyZmhjG5b5VsJdcMWnd2d/SI+RcYumI1PK8zBYqNQ==[/tex].[br][/br]
设 [tex=3.929x1.214]AWbQ/81wF3sYHzx+DT7PnrGXonKnyJG03SCBJZO0M+0=[/tex] 则 [tex=0.786x1.0]O9mrDPbtU/j67mXVbT2dlg==[/tex] 在 [tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex] 中有 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 个不同特征值当且仅当有 [tex=2.214x1.143]v8mnZ12+ZL3wvk5cLchvyZqfP4n3ShCe2T0BD2Oh7Vo=[/tex] 中可逆矩阵 [tex=0.714x1.286]atrPPistVyxj7cY8rjePCQ==[/tex] 使 [tex=3.214x1.286]TjIo+3/SLoLuFbEKtgWeQbpSmdW1smUB7JsVtvKtSpI=[/tex] 为对角矩阵，且 [tex=5.357x1.357]NovbxKl63Ey/milqTcbe/6pqcNg08v6RCQYiCVf8gaKUu6JugEBILzWUBwmozpTBN7sCFfylfszratPA7v6+kA==[/tex] 为 [tex=0.786x1.0]O9mrDPbtU/j67mXVbT2dlg==[/tex] 的最低多项式.
设 [tex=3.929x1.214]AWbQ/81wF3sYHzx+DT7PnrGXonKnyJG03SCBJZO0M+0=[/tex] 则 [tex=0.786x1.0]O9mrDPbtU/j67mXVbT2dlg==[/tex] 在 [tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex] 中有 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 个不同特征值当且仅当有 [tex=2.214x1.143]v8mnZ12+ZL3wvk5cLchvyZqfP4n3ShCe2T0BD2Oh7Vo=[/tex] 中可逆矩阵 [tex=0.714x1.286]atrPPistVyxj7cY8rjePCQ==[/tex] 使 [tex=3.214x1.286]TjIo+3/SLoLuFbEKtgWeQbpSmdW1smUB7JsVtvKtSpI=[/tex] 为对角矩阵，且 [tex=5.357x1.357]NovbxKl63Ey/milqTcbe/6pqcNg08v6RCQYiCVf8gaKUu6JugEBILzWUBwmozpTBN7sCFfylfszratPA7v6+kA==[/tex] 为 [tex=0.786x1.0]O9mrDPbtU/j67mXVbT2dlg==[/tex] 的最低多项式.