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Lee
  • Member for 8 years, 6 months
  • Last seen more than a month ago
  • Hong Kong
13 votes
3 answers
451 views

Express $\mathrm{Tr}(X)$ in terms of $A$, given that $X=A^TX(I+X)^{-1}A$

6 votes
1 answer
208 views

Find all $x\in\mathbb{C^n}$ such that $||Ax||_2=1$ and $||x||_2=1$

6 votes
1 answer
276 views

Minimize $\mathrm{tr}(R^{-1}B^TXB)$ over $R$ subject to $X=A^TXA-A^TXB(R+B^TXB)^{-1}B^TXA$

5 votes
1 answer
256 views

Minimize $\mathrm{tr}(B^TXB)$ subject to $X=A^TX(I+BB^TX)^{-1}A$

5 votes
1 answer
260 views

Minimize $x^*(A+A^*)x$ such that $x^*A^*Ax=1$ and $x^*x=1$

5 votes
1 answer
67 views

Finding the least point of numerical range which lies on real axis

5 votes
1 answer
216 views

Ellipse bounded between two lines and a circle

5 votes
0 answers
298 views

Prove that $\mathrm{Tr}(B^\mathsf{T}Y^{-1}B)$ is independent of $B$

5 votes
2 answers
85 views

Find minimum number of figures needed , so that no additional figure can be added?

5 votes
1 answer
217 views

Express $\operatorname{trace}(B'XB)$ in terms of $A$ and $B$

4 votes
1 answer
347 views

Control system problem

4 votes
1 answer
148 views

Show that $4x^2-yz$ is a perfect square

4 votes
1 answer
275 views

Intuition behind the Law of large numbers

3 votes
0 answers
68 views

How to plot $S:=\{(\Re (x^*Ax),\Im(x^*Ax))\mid\|x\|_2=1,\|Ax\|_2=1\}$?

3 votes
0 answers
26 views

Given K s.t. $\frac{K+K^*}{2}=L^*L+I$ and $\frac{K-K^*}{2i}=\frac{L+L^*}{2}$, find $L$.

3 votes
1 answer
185 views

Solve $x^{x^{x^{2017}}}=2017$

3 votes
0 answers
66 views

Position of roots of a polynomial after the coefficients perturbation

3 votes
1 answer
167 views

Minimize $\mathrm{tr}(B'XB)$ where $X$ is solution for DARE

3 votes
2 answers
50 views

exponential inequality $\frac{2^{2C_1}+2^{2C_2}-1}{2^{2C_1}}\geq\frac{2^{2\hat{C_1}}+2^{2\hat{C_2}}-1}{2^{2\hat{C_1}}}$

3 votes
1 answer
274 views

What is the maximum value of $x^TAx$ subject to $x\in\{\pm1\}^n$?

3 votes
0 answers
58 views

What is $\max\limits_{\sum_{i=k}^{n}x_i\leq\sum_{i=k}^{n}y_i \\\forall k=1,2,\cdots,n} \prod_{i=1}^{n} x_i$

3 votes
1 answer
76 views

For any nonzero $A\in\mathbb{C}^{n\times n}$, there exist $x\in\mathbb{C}^n$, such that $x^*Ax\neq0$

3 votes
1 answer
248 views

Minimize $\mathrm{tr}(XX^T)$ subject to inequality constraints

2 votes
0 answers
153 views

Jordan Canonical Form of Nilpotent matrix

2 votes
1 answer
107 views

Prove that $x_1+x_2+\cdots+x_L\geq a_1x_1+a_2x_2+\cdots+a_nx_n$

2 votes
1 answer
97 views

How to find $\min\limits_{{X:\,det(I+X)\geq a}} tr(X\Sigma)$ given diagonal $\Sigma$ and real $a$?

2 votes
2 answers
118 views

Prove that dim$N(A^i)=i$ if $A$ is nilpotent

2 votes
1 answer
38 views

What is the center of ellipse given by $||Ax-x_c||_2\leq 1$?

2 votes
1 answer
171 views

Maximize $\det X$, subject to $X_{ii}\leq P_i$, where $X>0$

2 votes
1 answer
140 views

Minimizing $R_1^2+R_2^2$ subject to $RT=I$

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