I dont understand how to solve this problem. Please can you explain the solution clearly? I want to learn how to solve such problems. Thank you
I am reading "Introduction to smooth manifolds" by Lee and one place is very unclear for me: Let $P$ and $Q$ be any complementary subspaces of $V$ (which is an $n$-dimensional real vector space) of ...
Suppose that in canonical symplectic basis $e_1,e_2,f_1,f_2$ we have $$\Omega=pf_1^*\wedge f_2^*+qe_1^*\wedge e_2^*+r(e_1^*\wedge f_2^*+e_2^*\wedge f_1^*)+s(e_1^*\wedge f_1^*-e_2^*\wedge f_2^*)$$ Let ...
I was wondering if linear manifold is a pure algebraic concept? Here is its definition from planetmath: Suppose $V$ is a vector space and suppose that $L$ is a non-empty subset of $V$. If there ...