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Results tagged with linear-algebra
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user 120302
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
2
votes
2
answers
114
views
A linear equation problem related to projection
Let $v_1,\cdots,v_s$ be $s$ vectors in $\mathbb R^d$ such that every set of $d$ vectors are linearly independent. Let $x_1,\cdots,x_n$ be $n$ vectors in $\mathbb R^d$ that satisfy the following linear …
- 601
4
votes
2
answers
651
views
The maximal size of intersection of two sets
Let $S=\{1,2,\cdots,2n\}$, and $S_i \subseteq S(i=1,2,\cdots,n+1)$ be $n+1$ subsets, each of which contains half of the $2n$ elements, namely $|S_i|=n$. Consider the following expression:
$$M=\max_{1\ …
- 601
0
votes
1
answer
43
views
For an one-order Linear Recurrence of a vector sequence, does the corresponding item follow ... [closed]
Consider an one-order Linear Recurrence of a vector sequence, such as
$${\bf x}_{n+1}={\bf A}{\bf x}_n$$
where ${\bf x}_n \in \mathbb{R}^m (\forall n)$, and ${\bf A} \in \mathbb{R}^{m\times m}$ and ${ …
- 601