【题目】设M为线性空间X的子集,令$$ C _ { 0 } ( M ) = \sum _ { i = 1 } ^ { n } \lambda _ { i } x _ { i } x _ { i } \in M , \lambda _ { i } \geq 0 $$,$$ \sum _ { i = 1 } ^ { n } \lambda _ { i } = 1 $$,n为自然数...
{ 2 } } + 5 \geq 2 \sqrt { k ^ { 2 } \bullet \frac { 4 } { k ^ { 2 } } } + 5 = 9 $$, 当且仅当$$ k ^ { 2 } = 2 $$时取等号, 所以$$ 1 - \frac { 9 } { k ^ { 2 } + \frac { 4 } { k ^ { 2 } } + 5 } \in \left[ 0 ,...
Let X_i, i \geq 0 be independent and identically distributed random variables with probability mass function p(j)=P(X_i=j), j = 1, ..., m, \sum_{j =1}^m P(j) = 1 Find E[N], where N = min(...
**严谨证明:** **命题**:设 \( A \) 是 \( n \times n \) 实方阵,其所有特征值均为非负实数且等于奇异值(即 \( \lambda_i(A) = \sigma_i(A) \geq 0 \))。证明 \( A \) 是对称矩阵。 --- **证明步骤:** **1. 特征值与奇异值的关系** 由题设,\( A \) 的特征值 \( \lam...
It is observed that for \\(n \\geq 2\\) and \\(k = 1\\), a class of transit models of the universe are obtained. The model 2 belongs to the scenario of phantom energy (\\( \\omega > - 1\\)). We have observed the existence of type-III singularity in our model 2. Some...
$$ 显然,$$ X ^ { T } X > 0 , ( A X ) ^ { 7 } ( A X ) \geq 0 $$).故当$$ \lambda > 0 $$时,对任意非零向量,$$ X ^ { T } B X > 0 $$,所以实对 称矩阵 B是正定矩阵. 结果一 题目 设A是$$ m \times n $$实矩阵,I是n阶单位矩阵.令矩阵$$ B = \lamb...
$$ 显然,$$ X ^ { T } X > 0 , ( A X ) ^ { T } ( A X ) \geq 0 $$.故当$$ \lambda > 0 $$时,对任意非零向量,$$ X ^ { T } B X > 0 $$,所以实对 称矩阵B是正定矩阵. 结果一 题目 【题目】设A是m×n实矩阵,I是n阶单位矩阵.令矩阵 B=λI+A^TA 其中A为实...