1) 设[tex=0.786x1.0]3akNjptD8YqOes80TdtIxQ==[/tex]为一个[tex=0.643x0.786]1p65fe6CUUvpZ1I+2NvzNQ==[/tex]阶矩阵,且 [tex=3.357x1.286]++kzfxuS5o6+rSX/Wehzm6HiIUmN9SxtDnKnaW9RuMQ=[/tex]证明[tex=0.786x1.0]3akNjptD8YqOes80TdtIxQ==[/tex]可以分解成[tex=2.929x1.214]Fa7TdhMTD0V1JXc/nEODlw==[/tex]其中 Q 是正交矩阵,T 是一上三角矩阵:[tex=11.571x6.5]7auM7Vr/aTN5VapY2kSBSGsWdjZ3d6roIR3LlrQ5HlbWYcz/iDreESfeAzbnk5qTT7xJFIrwInmXHAz2Z5xNWiqS2ky1g1iRL6iRsHnUfeTUX3MIgNKBE0qvz/0q9P3WD158ekMUoihvmg6SYQLiU9mIj1z4pk2Ecnqx8u1WnKcgc/BNiZZ1xwOU3J9TnmOG[/tex]且[tex=7.857x1.357]JNSFq7IS4SpviK2aXb6i2K42Q9maB09od4czzykn46E=[/tex] ,并证明这个分解是唯一的;2)设 A 是 n 阶正交矩阵,证明存在一上三角矩阵 T,使[tex=3.714x1.286]iESqo3JiJ1nx/oVod/EBDQzmz4O3io3a53sTULJ4/W0=[/tex]
1) 设[tex=0.786x1.0]3akNjptD8YqOes80TdtIxQ==[/tex]为一个[tex=0.643x0.786]1p65fe6CUUvpZ1I+2NvzNQ==[/tex]阶矩阵,且 [tex=3.357x1.286]++kzfxuS5o6+rSX/Wehzm6HiIUmN9SxtDnKnaW9RuMQ=[/tex]证明[tex=0.786x1.0]3akNjptD8YqOes80TdtIxQ==[/tex]可以分解成[tex=2.929x1.214]Fa7TdhMTD0V1JXc/nEODlw==[/tex]其中 Q 是正交矩阵,T 是一上三角矩阵:[tex=11.571x6.5]7auM7Vr/aTN5VapY2kSBSGsWdjZ3d6roIR3LlrQ5HlbWYcz/iDreESfeAzbnk5qTT7xJFIrwInmXHAz2Z5xNWiqS2ky1g1iRL6iRsHnUfeTUX3MIgNKBE0qvz/0q9P3WD158ekMUoihvmg6SYQLiU9mIj1z4pk2Ecnqx8u1WnKcgc/BNiZZ1xwOU3J9TnmOG[/tex]且[tex=7.857x1.357]JNSFq7IS4SpviK2aXb6i2K42Q9maB09od4czzykn46E=[/tex] ,并证明这个分解是唯一的;2)设 A 是 n 阶正交矩阵,证明存在一上三角矩阵 T,使[tex=3.714x1.286]iESqo3JiJ1nx/oVod/EBDQzmz4O3io3a53sTULJ4/W0=[/tex]
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