Recent content by smile1

they are obtained by using the Gram-Schmidt orthogonalization, so I think they are basis automatically, if you want to prove that just using the definition of basis. Hope that helps.

Got it, thanks a lot:)

Hello everyone Here is the problem: Find the value $F(v,f)$ of the tensor $F=e^1\otimes e_2 +e^2\otimes(e_1+3e_3)\in T^1_1(V)$ where $v=e_1+5e_2+4e_3, f=e^1+e^2+e^3$ Does $e^1\otimes e_2=0$ in this problem?Thanks

Hello everyone I hope someone can check the solution for me. Here is the problem: Let $V=V_1\oplus V_2$, $f$ is the projection of $V$ onto $V_1$ along $V_2$( i.e. if $v=v_1+v_2, v_i\in V_i$ then $f(v)=v_1$). Prove that $f$ is self-adjoint iff $<V_1,V_2>=0$ my solution is this...

Yes, you are right, actually the normalization is not hard.

I think we need to find the eigenvectors for this matrix, then we can use them to diagonalize this matrix. But the problem is that I am not sure wether we need to normalize those eigenvectors or not. If we do, it is not easy to normalize them.

Hello everyone Here is the question Find the distance from a vector $v=(2,4,0,-1)$ to the subspace $U\subset R^4$ given by the following system of linear equations: $2x_1+2x_2+x_3+x_4=0$ $2x_1+4x_2+2x_3+4x_4=0$ do I need to find find a point $a$ in the subspace $U$ and write the vector $a-v$...

Hello everyone, I stuck on this problem: find the dimension of the space of dimension of the space of skew-symmetric bilinear functions on $V$ if $dimV=n$. I thought in this way, for skew-symmetric bilinear functions, $f(u,v)=-f(v,u)$, then the dimension will be $n/2$ Am I right? thanks

Hello everyone Here is the question Find positive and negative indexes of inertia for the function $q(x)=TrX^2$ on the space $M_n(R)$ I did some work, first I suppose $X$ as a n by n matrix, then $TrX^2=a_{11}^2 +...+a_{nn}^2+2(a_{ij}a_{ji})$ It seems like that all terms are positive...