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Results tagged with linear-algebra
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user 21816
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
17
votes
1
answer
4k
views
Geometric interpretations of matrix inverses
$A$ is an invertible $n \times n$ matrix. Interpret each row of $A$ as a point in $\mathbb{R}^n$; then these $n$ points define a unique hyperplane in $\mathbb{R}^n$ that passes through each point (th …
- 4,713
10
votes
2
answers
3k
views
How do you tell if a system of linear inequalities has a solution?
A naive solution would be to optimize a dummy variable via linear programming and see if a result is returned. I imagine there must be a more direct way.
- 2,239
2
votes
2
answers
332
views
How do you tell if the span of a set of vectors enters the most positive sector of a graph?
I have $k$ linearly independent vectors in $\mathbb{R}^n$. I want to know if the span of these vectors (i.e. the set of points in $\mathbb{R}^n$ that can be described by linear combinations of these …
- 54.2k