3
votes
1answer
92 views

submatrix of a given size with maximum frobenius norm

Let $I\subset \{1,2,\ldots,n\}$, and let $|I|$ denote its cardinality. Now given a Hermitian matrix $\mathbf{A}\in\mathbf{C}^{n\times n}$. I am interested in finding the subset $I$ that maximizes the ...
0
votes
1answer
342 views

eigen-decomposition solution? is it unique?

Assume an N*N covariance matrix (Q) which is a positive definite matrix. The decoder X is assumed to be N*s, where s<=N. X is calculated to be s eigenvectors corresponding to s minimum eigenvalues. ...
1
vote
0answers
224 views

Totally Uni-modular Matrices

A matrix is totally uni-modular if the determinant of any (square) sub-matrix is {+1, 0, -1}. My question is, "Is there a way to transform(linear or non) a general matrix into a totally uni-modular ...
2
votes
0answers
168 views

Could SVD be used to optimize the partial inner-products?

Suppose a set $N$ of $n$ distinct points in $m-$dimensional space is given in $X\in\mathbb{R}^{n\times m}$. Also, suppose a subset $L\subset N$, $|L|=l<m<n$, with $m-$dimensional coordinates in ...
2
votes
2answers
200 views

Maximization of a matrix product by iterative methods

This might not be very difficult, but I think I may have gotten a little confused. Suppose we are given a matrix A, and would like to find the vector x of modulus 1 which maximises the product xt A x ...
3
votes
4answers
528 views

efficient way to compute the inversion of the following matrix

Hi, there I have looked it up in the current textbook. The conventional numerical method to compute the inversion of an $n \times n$ matrix requires $O(n^3)$. However, for the following special ...