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Results tagged with symplectic-group
Search options answers only
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user 13972
5
votes
Accepted
Symplectic form on the third symmetric power of a plane
There's nothing miraculous about this: Here is an explicit formula: Let $x$ and $y$ be a basis for $V$. Then $A,B\in S^3(V)$ can be written in the form
$$
A = a_{-3}\,x^3+3a_{-1}\,x^2y+3a_1\,xy^2+a …
- 108k
27
votes
Accepted
Alternate and symmetric matrices
I feel that framing this question in terms of matrices rather than bilinear forms on a vector space obscures what is actually going on and makes it harder to understand what needs to be proved. Here …
- 108k
6
votes
Accepted
Symplectic block-diagonalization of a complex symmetric matrix
This fails even for $n=1$. In this case, the matrix
$$
A = \begin{pmatrix} 1&0\\0&0\end{pmatrix}
$$
can't be diagonalized in the form that you want because it's not zero, yet its determinant vanishes …
- 108k