1,076 reputation
719
bio website
location
age
visits member for 3 years, 8 months
seen Jul 23 '13 at 15:47

May
1
comment Fun Linear Algebra Problems
@Moron: ok, unfortunately the only time I saw $F_2$ was to assume the exact opposite, so I have no idea how that helps. Also, I assume it's obvious but an inhabitant can be a member of several clubs? (otherwise it seems trivial)
May
1
comment Fun Linear Algebra Problems
I'm having some trouble solving this with my linear algebra knowledge, any hints? (also, just so I'm sure, what does $\mathbb{F}_{2}$ mean?)
Apr
20
comment Spectral decomposition of a normal matrix
@Arturo: I'm stuck after finding the eigenspaces. I got $$V_{\lambda_1}=sp{(\frac{1}{\sqrt 2}, 0, \frac{1}{\sqrt 2})}, V_{\lambda_2}=sp{(\frac{-1}{\sqrt 3}, \frac{1}{\sqrt 3}, \frac{1}{\sqrt 3})}, V_{\lambda_3}=sp{(\frac{-1}{\sqrt 6}, \frac{-2}{\sqrt 6}, \frac{1}{\sqrt 6})}$$ And I know that if $v=v_1+v_2+v_3, v_i \in V_{\lambda_i}$ then $P_i = v_i$. But how do I actually find $[P_i]$? I'm confused.
Apr
19
revised Spectral decomposition of a normal matrix
fixed error
Apr
19
asked Spectral decomposition of a normal matrix
Apr
13
comment Norm of a symmetric matrix?
Ross, how is your last sentence justified? Also I'm not entirely sure I got it right, what did you mean by "...input vector is along the eigenvector associated with the largest eigenvalue."? Which eigenvector? if $v=\alpha_1 v_1 +...+\alpha_n v_n$ is the input vector as you put it, then it's a linear combination of eigenvalues where $||v||=1$. What are you arguing about $||Av||$?
Mar
31
accepted Multiplication of block matrices
Mar
31
asked Multiplication of block matrices
Mar
26
comment Adjoint of a linear transformation in an infinite dimension inner product space
I tried understanding the links you provided but I'm still in doubt: is it possible to find an infinite inner product space and a linear transformation $T$, such that no linear transformation $S$ exists such that $(Tv, u)=(v, Su)$?
Mar
26
comment Adjoint of a linear transformation in an infinite dimension inner product space
Thanks. I'm indeed unfamiliar with Hilbert spaces. I was trying to think of $R[x]$ with the inner product $\int_{a}^{b} f(x)g(x)dx$.
Mar
26
asked Adjoint of a linear transformation in an infinite dimension inner product space
Mar
25
comment Conjugate-transpose of a linear transformation
Yes that's what I meant.. Or transformation matrix. Thanks.
Mar
25
comment Conjugate-transpose of a linear transformation
Or simply find the transformation basis of $T_{P}$ and take its transpose-conjugate, which should yield the same result.
Mar
25
comment Conjugate-transpose of a linear transformation
Thanks for the detailed explanation. Given a certain matrix $P$, to find the transformation basis of $(T_{P})*$ in the standard basis, I need to simply find the transformation basis of $T_{K}$ where $K=P^*$, right? (based on the above)
Mar
25
accepted Conjugate-transpose of a linear transformation
Mar
25
revised Conjugate-transpose of a linear transformation
added 36 characters in body; deleted 1 characters in body
Mar
25
asked Conjugate-transpose of a linear transformation
Mar
24
revised Question regarding positive-definite matrices
changing transpose to transpose-conjugate
Mar
24
suggested suggested edit on Question regarding positive-definite matrices
Mar
14
revised Regarding orthonormal basis
added 188 characters in body