# Questions tagged [systems-of-equations]

This tag indicates that several equations (of some type) must all hold. Do not use alone! Use in conjunction with (linear-algebra), (polynomials), (pde), (differential-equations), (inequalities) or another tag that describes the nature of the equations being considered.

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### Solving complicated system of equations

Suppose I have the general equation like $$a_j = -(k+\sum_{i\neq j}^n\alpha_iba_i)^{-1},$$ where $j=1,\cdots,n$ and $\alpha_i,k$ are constants for $i=1,\cdots,n$ and $\sum_{i=1}^n\alpha_i=1$ Is there ...
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### How to know if a system of equations of the form $y_i = \sum_{j=0}^{n} c_j e^{jx_i}$ is solvable

I was working on a problem and faced a this system of equations ($y_i$ and $x_i$ are givens) $$y_i = \sum_{j=0}^{n} c_j e^{jx_i} \quad0 \le i \le n$$ is there a way to determine this system is ...
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### LSQR method for solving a linear equation with positive value constraint for one column of the solution

I am solving an overdetermined sparse linear problem (Ax= B) using a C code. The code is using the LSQR method to find the solutions. There are 6 unknowns for every equation. One of the solutions is a ...
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### On the solution space of linear matrix equations.

Consider a linear matrix equation $$Y = \sum_{i} A_i X B_i^T = \sum_i (B_i\otimes A_i) \cdot X = T\cdot X$$ When does the solution space admit a basis consisting only of rank-1 matrices?
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### Analysis of a particular instance of a non-linearsystem of equations

Consider a vector space $V \in \mathbb{R}^n$. Given a set of $\frac{1}{2}n(n-1)$ square matrices $\{\boldsymbol{A}^{(ij)}\}_{ij}$ (where $(\boldsymbol{A}^{(ij)})^T = \boldsymbol{A}^{(ji)}$), how do we ...
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### Using $u(t,\gamma(t,x))=\gamma_t(t,x)$ to find various partial derivatives of $\gamma$ in terms of $u$

I have two functions $u:\mathbb{R}\times S^1\rightarrow S^1$ and $\gamma:\mathbb{R}\times S^1\rightarrow S^1$ related via this composition $u(t,\gamma(t,x))=\gamma_t(t,x)$ (call this equation $(1)$), ...
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### Constants for inhomogeneous system of ODE

For a first order inhomogeneous ODE we've got a formula $$\displaystyle{y(x) = Y(x)\,\left[c_0+\int_{x_0}^{x}Y^{-1}(x)\,b(x)\,\mathrm{dx}\right]},$$ where $Y(x)$ is that fundamental matrix ...
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