Samrat Mukhopadhyay
  • Member for 7 years, 1 month
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  • India
Inverse of particular lower triangular matrix
5 votes

One observation: $$A = I+L,$$ where $L$ is a lower triangular matrix with $0$ in the diagonals. This matrix $L$ can be seen to satisfy $L^n=0$, and $L^j\ne 0,\ 1\le j\le n-1$. Thus, one can write $$A^...

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Inverting (via Taylor expansion) a sum of (rank-deficient) skew-symmetric matrix and (rank-deficient) Diagonal matrix
Accepted answer
4 votes

Just an idea. I think the best way to start is to expand on the structure of the matrices $D, C$. For example, $D$ can be readily seen to be expressible in the form $$\alpha M_1\otimes I_2=\alpha\...

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minimum information distribution given moments of its square
Accepted answer
4 votes

Let us consider the special case when $\mu$ is the Lebesgue measure on $\mathbb{R}$. The derivation then should be extendable to the general case without much effort. We need to find the distribution ...

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A good starting position for maximizing a function with Newton-Raphson / Halley's method
1 votes

You can try applying gradient ascent method and run it for a few iterations to get an initial guess for $\mathbf{t}$. As the function is strongly concave, the gradient ascent is sure to converge to ...

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