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Results tagged with linear-algebra
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user 4344
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
11
votes
Accepted
Largest rank submatrix of a skew symmetric matrix
Yes. Suppose that you have a general $n \times n$ matrix M. The coefficient of $(-x)^k$ in the characteristic polynomial is the sum of all the principal minors of the matrix of size n-k. From this it …
- 5,137
10
votes
Accepted
Quadratic forms over finite fields
I will sketch below a standard argument to show what you need, because I find it very neat!
Let $V$ be a finite dimensional vector space over a field $k$ and let $q \colon V \to k$ be a quadratic for …
- 5,137