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Feb
28
comment Finding a similarity transform for a matrix that minimizes the (2-norm) condition number
Hmmm... how does this answer my original question about condition number? If similarity transforms minimize the $||B||$, why does that mean they also minimize $||B^{-1}||$?
Feb
12
comment simple example of recursive least squares (RLS)
Points for a practical short example... but I need some understanding, and throwing code at me, even simple code that I can read and translate to matrix algebra, doesn't help with that understanding.
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
comment constrained complex number equation requiring imaginary part to be zero
yes (I'm an EE)
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
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
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
1
comment Is there a faster algorithm than $O(n^2)$ for calculating “cofactors” $C_k = \prod\limits_{j\neq k}(c_k - c_j)$?
could you elaborate?
Jan
1
comment Is there a faster algorithm than $O(n^2)$ for calculating “cofactors” $C_k = \prod\limits_{j\neq k}(c_k - c_j)$?
yeah, vectorization is another option. (I'm using numpy in my case.) But the polynomial coefficients are huge and are ill-conditioned; I have to work with the roots directly in order to keep numerical errors low.
Dec
19
comment solving a series of nonlinear equations for the zeros of Bessel polynomials
more info on Bessel polynomials at dlmf.nist.gov/18.34
Dec
18
comment roots of Padé approximating polynomials to the exponential function
and Gonnet/Guettel/Trefethen's paper which also seems very relevant but I can't figure out how to apply it: guettel.com/download/gonnet_guettel_trefethen.pdf which I
Dec
18
comment roots of Padé approximating polynomials to the exponential function
Then we have Saff and Varga's paper On the Zeros and Poles of Padé Approximants to $e^z$ which looks tantalizingly relevant, but they don't compute the roots numerically, they just have proofs of general behavioral of where they are and aren't.
Dec
17
comment Eigenvectors of special matrix with characteristic polynomial
correct, i had intended to include "monic" and somehow skipped it. Edited question.
Dec
17
comment Finding a similarity transform for a matrix that minimizes the (2-norm) condition number
and P is just any matrix of eigenvectors of A? (as per en.wikipedia.org/wiki/Diagonalizable_matrix) I guess this is implied by $AV=V\Lambda \rightarrow V^{-1}AV = \Lambda$ en.wikipedia.org/wiki/…
Dec
17
comment Finding a similarity transform for a matrix that minimizes the (2-norm) condition number
interesting... are there invertible matrices that are not diagonalizable?
Dec
15
comment Can some clearly explain about lim sup and lim inf?
dumb question: are inf and sup just fancy math names for min and max?
Nov
9
comment Explanation of Chandrupatla's algorithm for root finding?
you're right on the consecutiveness, although I can't quite tell which is which. (I think c is the newest, not positive though)