# Questions tagged [linear-algebra]

Questions about the properties of vector spaces and linear transformations, including linear systems in general.

3,709 questions
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### Problem of percentages [closed]

Can someone explain why: 100% of 10 = 10% of 100 or 78% of 5 = 5% of 78 I don't seem to understand why this relationship occurs and have tried to solve it algebraically
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### Relationship between $2 \to 2$ norm and $\infty \to 2$ norm [closed]

I am wondering what are the best known relationship between $\|A\|_{2\rightarrow 2}$ and $\|A\|_{\infty\rightarrow 2}$ and how tight it is. E.g., the trivial result is that for matrix $A$ with ...
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### $SO(m+1)$-equivariant maps from $S^m$ to $S^m$

Let $G=SO(m+1)$ , $m \geq 2$, act in the standard way on $S^m$. Let $F:S^m \to S^m$ be a $G$-equivariant map, i.e., $g F(g^{-1}x) =F(x)$ for all $x \in S^m$ and $g \in G$. Question 1: Is F the ...
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### Solving diagonal simultaneous quadratic equations

A problem I am trying to solve has led to me to the following system of equations: $$A(x^2) + Bx + c = 0$$ Where $A$ and $B$ are known matrices, $c$ is a known vector, $x$ is the vector of unknowns ...