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3
votes
1answer
197 views

The existential theory of the reals

Some definitions of the existential theory of the reals (ETR) allow a real closed field and some definitions allow only rational numbers as coefficients of polynomials. Which one is correct? Will the ...
3
votes
0answers
113 views

Gaussian Elimination in terms of Group Action

Gaussian elimination makes determinant of a matrix polynomial-time computable. The reduction of complexity in computing the determinant, which is otherwise sum of exponential terms, is due to presence ...
10
votes
1answer
263 views

What is the largest tensor rank on matrix.

A tensor rank of tree dimentional matrix $M[i,j,k], i,j,k\in [1,\ldots,n]$ is a minimal number of vectors $x_i,y_i,z_i$, such that $M=\sum_{i=1}^d x_i\otimes y_i\otimes z_i$. From dimension argument ...