# Questions tagged [matrix-equations]

This question is about equations where the unknown itself is a matrix such as Sylvester or Riccati equations. For systems of linear equations (where the unknown is a vector), use "linear-system".

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### Assume $AX = C$. How to determine which entry of $BX - D$ is non-negative?

Let $A,B$ be $n \times n$ matrices and $C,D$ be $n \times 1$ matrices. Moreover, all entries of $A,B,C,D$ are non-negative. Assume that there is a unique matrix $X$ that solves $AX = C$. My goal is ...
88 views

### Finding derivative of Matrix at different grid points using Finite difference methods/ Cholesky Factorization

I want to code this problem in MATLAB. It would be a huge help if someone can suggest to me how I can approach it. I need to solve the below-highlighted equation, I need ...
61 views

### implementation for coppersmith matrix multiplication

Is there any online implementation for the coppersmith matrix multiplication I have searched alot but can not find any? and if there is not any why is that Isn't this algotithm much faster than ...
171 views

### Solving $AXB + X\odot C = D$ matrix equation

Can anyone see a way to solve this equation efficiently? $$AXB + X\odot C = D$$ I tried a straightforward solution that involved vectorizing $X$ but that turned out too expensive for my application -...
148 views

### Maximize a function of an orthogonal matrix

I'm trying to write up a small code that, given a set of normal vibrational modes for a molecule, will convert them to localized vibrational modes. To do this I'm following the procedure from J. Chem. ...
128 views

### Eigenvalue-like problem with coupled ODEs

I am looking at the following system of ODEs: \begin{array}{r}{\left[c_{2}(k)-\partial_{\tau}^{2}\right] \varphi_{2}\left(\tau \right)=f_{21}(\tau) \varphi_{1}\left(\tau \right)} \\ {\left[c_{1}(k)-...
176 views

### Mass Matrix and how to handle it (ODEs) - References

I'm interested in a good reference/paper about how to handle numerically a mass-matrix system as \begin{align} \mathbf{M}(t,y)\dot{y} =F(y,t) \end{align} I know that such a problem can be solved by ...
138 views

### Solving linear system with matrix multiplication

When solving a linear system $Ax=b$ where $A=B^TCB$ do I need to form $A$ explicitly by two matrix-matrix multiplications or is there another more simple way? $C$ is a NxN matrix and not always ...
310 views