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Jan
13
asked numerically obtaining relative condition number of a monic polynomial with respect to finding its roots
Jan
4
revised B and C matrices for real modal representation of a 2x2 linear system with complex eigenvalues
added 134 characters in body
Jan
4
accepted constrained complex number equation requiring imaginary part to be zero
Jan
4
comment constrained complex number equation requiring imaginary part to be zero
That's interesting; that tells me that my initial constraint of $|k_1| = |k_2| = 1$ can't always be met. (e.g. if $b_1 = 2+3j$ and $b_2 = 4+5j$); also that if I have one solution $(k_1,k_2)$ then $(k_1e^{j\theta}, k_2e^{-j\theta})$ is also a solution.for any arbitrary $\theta$.
Jan
3
revised constrained complex number equation requiring imaginary part to be zero
added 23 characters in body
Jan
3
comment constrained complex number equation requiring imaginary part to be zero
yes (I'm an EE)
Jan
3
asked constrained complex number equation requiring imaginary part to be zero
Jan
3
answered B and C matrices for real modal representation of a 2x2 linear system with complex eigenvalues
Jan
3
revised B and C matrices for real modal representation of a 2x2 linear system with complex eigenvalues
edited tags
Jan
3
revised B and C matrices for real modal representation of a 2x2 linear system with complex eigenvalues
added 260 characters in body
Jan
3
comment Prove that, $a^2b(a-b)+b^2c(b-c)+c^2a(c-a) \geq 0.$
you skipped one point, namely that you have to show $A, B, C$ are all nonnegative. (which is implied by the triangle inequality)
Jan
3
revised B and C matrices for real modal representation of a 2x2 linear system with complex eigenvalues
added 797 characters in body
Jan
3
asked B and C matrices for real modal representation of a 2x2 linear system with complex eigenvalues
Jan
3
comment similarity transform mapping diagonal matrix of complex conjugates, to real matrix
where does the matrix in your sentence "In particular, calculate the first eigenvector" come from? Is that $A-\lambda I$ for $\lambda = a+bj$?
Jan
3
comment similarity transform mapping diagonal matrix of complex conjugates, to real matrix
well, I've been searching the web, but I have Strang's Intro to Linear Algebra.
Jan
3
accepted similarity transform mapping diagonal matrix of complex conjugates, to real matrix
Jan
3
comment similarity transform mapping diagonal matrix of complex conjugates, to real matrix
excellent -- thanks! I would have thought discussions of diagonalization and block diagonalization and similarity transforms would include this, but I didn't see any mention of it.
Jan
3
comment similarity transform mapping diagonal matrix of complex conjugates, to real matrix
really?! weird.
Jan
3
comment similarity transform mapping diagonal matrix of complex conjugates, to real matrix
Oh. Huh, that seems too easy. Is there a way to express it directly in terms of $a$ and $b$? I figure it would help to express them in polar form as $a=r \cos \theta$ and $b = r \sin \theta$.
Jan
3
asked similarity transform mapping diagonal matrix of complex conjugates, to real matrix