daniel.jackson
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 May28 suggested approved edit on Positive semidefinite quadratic form May28 asked Positive semidefinite quadratic form May2 comment Fun Linear Algebra Problems @Moron: very nice, got it :). May1 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) May1 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?) Apr20 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. Apr19 revised Spectral decomposition of a normal matrix fixed error Apr19 asked Spectral decomposition of a normal matrix Apr13 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 $||Av||$? Mar31 accepted Multiplication of block matrices Mar31 asked Multiplication of block matrices Mar26 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 $(Tv, u)=(v, Su)$? Mar26 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 $\int_{a}^{b} f(x)g(x)dx$. Mar26 asked Adjoint of a linear transformation in an infinite dimension inner product space Mar25 comment Conjugate-transpose of a linear transformation Yes that's what I meant.. Or transformation matrix. Thanks. Mar25 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. Mar25 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) Mar25 accepted Conjugate-transpose of a linear transformation Mar25 revised Conjugate-transpose of a linear transformation added 36 characters in body; deleted 1 characters in body Mar25 asked Conjugate-transpose of a linear transformation