# Tagged Questions

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### If $A\ne 0$ is a square matrix over a commutative ring with $\det A=0$, then its null space contains an element whose components are minors of $A$

Let $R$ denote a commutative ring and $A\ne 0$ a $n\times n$ matrix over $R$ with $\det A=0$. Then there exists a $x\in\ker A\setminus\left\{0\right\}$ such that all components of $x$ are minors of ...
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### Some questions about similar matrices

Two matrices A and B are similar, if and only if there exists an invertible matrix C with $A=C^{-1}BC$. A necessary condition for the similarity is, that the characteristic polynomials coincide. I ...
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### Computing the decomposition of a representation of $S_n$

I have an explicitly defined representation of the symmetric group that I would like to decompose into irreducibles. How to do this most easily? The best approach I have so far is as follows: Find a ...
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### Using Wolfram Alpha to solve a system of linear equations

How do I input the below system of equations in Wolfram Alpha in order to solve for the unknowns? I'm wondering if there's some kind of code that can be written in order to make wolfram alpha ...
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### Flatten kronecker product in CAS?

I am a new user of Maxima, and I need to trace the elements of a big messy kronecker product of symbolic matrices. I tried the following to get my feet wet, but I don't get a simple, flat matrix -- ...
### solving a matrix equation $X-I=a \cdot (X\cdot U^T + U \cdot X)$
I am trying to solve the $n \times n$ diagonal matrix $X$ in the following equation: $$X-I=a \cdot (X\cdot U^T + U \cdot X)$$ where $0<a<1$ is a given scalar, $U$ is a $n \times n$ given ...