All Questions
8
questions
3
votes
1
answer
201
views
How to find a unimodular integer matrix $T$ satisfying $T^\top A T=B$ given symmetric integer matrices $A,B$?
Given two unimodular symmetric integer matrices $A$ and $B$,
I asked how to find a unimodular integer $T$ that satisfies this nonlinear relation between $T$ and $A,B$ like this in Mathematica:
...
- 251
8
votes
2
answers
388
views
Given square matrices A and B, how to solve T obeys Transpose[T]. A . T = B?
Dear Mathematica experts,
Given two square matrices, A and B, how do we use Mathematica to solve a matrix T such that T satisfies this matrix equation? (Here we have A,B,T $\in$ general linear matrix ...
- 251
0
votes
0
answers
49
views
Optimization problem with complex and real values
I have the following optimization problem:
$\underset{{{a}_{1}},...,{{a}_{m}}}{\mathop{\max }}\,\parallel \sum\limits_{n=1}^{N}{{{a}_{n}}}{{\varpi }_{n}}{{e}^{j{{\theta }_{n}}}}{{\varphi }_{n}}{{\...
4
votes
0
answers
137
views
Solving or Minimizing the Norm of the matrix equation $M^TAM - M^TB - B^TM =C$
I am trying to solve the matrix equation $M^TAM - M^TB - B^TM=C$ where I know A, B and C. My unknown matrix is M which has the special form that all the rows and columns sum to zero.
i.e. I have four ...
- 777
2
votes
1
answer
129
views
How to grab two points from linear equations and from a matrix m.x == b for the purpose of creating lines or planes from each row.?
Don't get me wrong I can easily do it on paper and I could probably write convoluted code that will get the job done but I feel like there has to be an easy Mathematica way to do this. A few users on ...
- 2,467
3
votes
1
answer
747
views
Solve the vector-matrix equation. Minimize the length of the desired n-dimensional vector
There is the following vector-matrix equation:
$$\mathbf x^\top\mathbf M\mathbf x=\begin{bmatrix}x_1&x_2&x_3\end{bmatrix}\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}...
- 2,444
1
vote
1
answer
228
views
Optimizing matrix inequalities over trace
I need to solve the following problem.
Given $n \times n$ Hermitian matrices $A\geq 0$ and $B_1, ~ B_2$ (need not be positive semidefinite), with $Tr(AB_1)<0~,Tr(AB_2)<0$ construct a ...
- 601
3
votes
1
answer
216
views
Decomposing a diagonal positive real matrix
I would like to 'decompose' a diagonal positive real matrix $E$ of rank $D$ onto $\sum_{i=1}^{D}c(i)N^i$:
$$E = \left(
\begin{array}{ccc}
0 & & & \\
& a & & \\
&...
- 677