设[tex=5.143x1.357]yCmyZ/PU0vubHyTDU0620dXJLnwnAW5rH4GV//SlR1A=[/tex]证明: 存在可逆矩阵 [tex=6.143x1.357]K69vB0InIAke18Ctk1v5iUM33WMWQqDU/2UbgrO8DX8=[/tex]使 [tex=3.0x1.214]3LPwI+Ms8uWX4W/wZJKnrQ==[/tex]为上三角矩阵.
设[tex=5.143x1.357]yCmyZ/PU0vubHyTDU0620dXJLnwnAW5rH4GV//SlR1A=[/tex]证明: 存在可逆矩阵 [tex=6.143x1.357]K69vB0InIAke18Ctk1v5iUM33WMWQqDU/2UbgrO8DX8=[/tex]使 [tex=3.0x1.214]3LPwI+Ms8uWX4W/wZJKnrQ==[/tex]为上三角矩阵.
求正交矩阵[tex=0.929x1.214]RjlejK6D6JSwVAeYdCSJQw==[/tex]使[tex=3.0x1.214]3LPwI+Ms8uWX4W/wZJKnrQ==[/tex] 为对角形, 设[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]为下列矩阵:[tex=8.643x3.929]jcCMHflCR8OS9TosV6N5vIzc2tkKBN1JF0Bu2m5z5oXb26CJagCEXy2U05qLmCZ6L7GdSVFLbl7gy/oTb7iFB1QaiTJ4QSrKJEirM7t5Z5uwATJk+MHibuktErDnr2k7[/tex]
求正交矩阵[tex=0.929x1.214]RjlejK6D6JSwVAeYdCSJQw==[/tex]使[tex=3.0x1.214]3LPwI+Ms8uWX4W/wZJKnrQ==[/tex] 为对角形, 设[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]为下列矩阵:[tex=8.643x3.929]jcCMHflCR8OS9TosV6N5vIzc2tkKBN1JF0Bu2m5z5oXb26CJagCEXy2U05qLmCZ6L7GdSVFLbl7gy/oTb7iFB1QaiTJ4QSrKJEirM7t5Z5uwATJk+MHibuktErDnr2k7[/tex]
对于下列实对称矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]，求正交矩阵[tex=0.643x1.0]iollMFTzm3iqFEHRyKQe1A==[/tex]，使[tex=3.0x1.214]3LPwI+Ms8uWX4W/wZJKnrQ==[/tex]为对角矩阵：[tex=8.571x3.643]3BT1BgBZQ5uJXxD5dg+w26muwh1xN1sRXO8Q3eF5f+iXIsfuTxHnjB5FW20E+IlcYCsQlk+1StM0NRY/eomQlo81btRtBoRS83IigXhahzWkoOaSWLYzjrUkt9UPITWH[/tex].
对于下列实对称矩阵[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]，求正交矩阵[tex=0.643x1.0]iollMFTzm3iqFEHRyKQe1A==[/tex]，使[tex=3.0x1.214]3LPwI+Ms8uWX4W/wZJKnrQ==[/tex]为对角矩阵：[tex=8.571x3.643]3BT1BgBZQ5uJXxD5dg+w26muwh1xN1sRXO8Q3eF5f+iXIsfuTxHnjB5FW20E+IlcYCsQlk+1StM0NRY/eomQlo81btRtBoRS83IigXhahzWkoOaSWLYzjrUkt9UPITWH[/tex].
设[tex=6.5x1.357]+5uKxqHZrQVy4BsAbSUB0JfceeMC1gQu6T7NS1Z/3ng=[/tex]且[tex=4.143x1.0]4EGwtNPILOTkGljLrP4Ukw==[/tex] 证明: 如果[tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex]都可对角化, 则存在可逆矩阵[tex=5.143x1.357]wctIloapZ7ZrNz25mC9AU0NFZWDC6XRvwhLLP84j2I4=[/tex]使[tex=3.0x1.214]3LPwI+Ms8uWX4W/wZJKnrQ==[/tex]与[tex=3.0x1.214]vgAu9voWF4OJ+yuNu+VaNA==[/tex]同为对角矩阵.
设[tex=6.5x1.357]+5uKxqHZrQVy4BsAbSUB0JfceeMC1gQu6T7NS1Z/3ng=[/tex]且[tex=4.143x1.0]4EGwtNPILOTkGljLrP4Ukw==[/tex] 证明: 如果[tex=2.0x1.214]vnzjVhyzo/NIhVUgFyjLlA==[/tex]都可对角化, 则存在可逆矩阵[tex=5.143x1.357]wctIloapZ7ZrNz25mC9AU0NFZWDC6XRvwhLLP84j2I4=[/tex]使[tex=3.0x1.214]3LPwI+Ms8uWX4W/wZJKnrQ==[/tex]与[tex=3.0x1.214]vgAu9voWF4OJ+yuNu+VaNA==[/tex]同为对角矩阵.