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Results tagged with linear-algebra
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user 9896
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
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Forming orthogonal bases in different orders
Let $\alpha_1, \dots, \alpha_n$ be unit vectors in some vector space $V = R^d$. For any permutation $\pi: [n] \rightarrow [n]$, we can form the Gram-Schmidt orthogonal bases $\beta_{\pi,1}, \dots, \be …
- 3,475
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Lower Bound on the Cost of Solving Linear System
Any $O(N^t)$ algorithm for matrix multiplication yields a corresponding $O(N^t)$ algorithm for matrix inversion. There are not any non-trivial lower bounds for matrix multiplication. It is believed th …
- 3,475
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When is polytope compatible with network flow?
A linear program is the problem of optimizing an linear objective function within some polytope $A$ over $\mathbf R^n$. My question is motivated by the question of when a linear programming problem ca …
- 3,475