矩阵
$f计算:$$f(14中山大学一)$设$n$阶实方阵$A$的主对角元为0,其余元为1
(1)求$|A|$及${A^{ - 1}}$ (2)求$A$的特征值,特征向量及最小多项式
$f计算:$设$A = left( {egin{array}{*{20}{c}}1&1&1 \ 1&1&1 \ 1&1&1 end{array}} ight)$,求矩阵$B$,使得${B^*} = A$
$f计算:$
标准形
$f计算:$设$left{ {egin{array}{*{20}{c}}
{{x_{n + 1}} = {x_n} + 4{y_n}}\
{{y_{n + 1}} = 2{x_n} + {y_n}}
end{array}}
ight.$,已知${x_0} = 1,{y_0} = 0$,求${x_{100}},{y_{100}}$
$f计算:$$f(06中科院四)$设$a$为实数,$A = left( {egin{array}{*{20}{c}}a&1&{}&{}\{}&a& ddots &{}\{}&{}& ddots &1\{}&{}&{}&aend{array}} ight) in {R^{100 imes 100}}$,求${A^{50}}$第一行元素之和
二次型
$f计算:$求实二次型$f(x_1,cdots,x_n)=sumlimits_{i=1}^n(x_i-sumlimits_{j=1}^ndfrac{x_j}{n})^2$的矩阵及正负惯性指数
$f计算:$$f(12浙大六)$设二次型$f({x_1}, cdots ,{x_n}) = sumlimits_{i = 1}^m {{{left( {{a_{i1}}{x_1} + {a_{in}}{x_n}} ight)}^2}} $,
(1)求二次型的方阵 (2)当$a_{ij}$均为实数时,给出二次型正定的条件
1
$f计算:$