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

2 votes
0 answers
110 views

Can the absolute value of fixed sized minors be arbitrarily ordered?

In an $m \times n$ matrix $X$, there are exactly $\binom{m}{r}\binom{n}{r}$ minors of size $r \times r$. Is it always possible to construct a real matrix $X$ such that the absolute value of the determ …
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2 votes
0 answers
70 views

What are desirable properties that data should satisfy to reasonably use the dynamic mode de...

In the dynamic mode decomposition, we consider a sequence of data vectors $\{z_0, \dots, z_m\}$ where $z_k \in \mathbb{R}^n$ for all $n$. We assume that the data satisfies the linear relationship $z_{ …
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