Skip to main content

All Questions

Filter by
Sorted by
Tagged with
1 vote
2 answers
86 views

Entrywise $\infty$-norm of squared difference of square roots of matrices

For a positive $n \times n$ definite real matrix $M$ we denote by $\sqrt{M}$ the positive square root of $M$. For an $n \times n$ matrix $A$ denote its entrywise infinity norm by $$\|A\|_{\infty,\...
ssss nnnn's user avatar
  • 177
9 votes
2 answers
1k views

$2$-norm distance between square roots of matrices

Suppose two square real matrices $A$ and $B$ are close in the Schatten 1-norm, i.e. $\|A-B\|_1=\varepsilon$. Can this be used to put a bound on the Schatten 2-norm distance between their square roots. ...
Pratik Rath's user avatar
4 votes
0 answers
205 views

Minkowski determinant inequality for the Fuglede-Kadison determinant

For positive-semidefinite matrices $A, B$ in $M_n(\mathbb{C})$, the Minkowski determinant theorem tells us that $\det(A+B)^{\frac{1}{n}} \ge \det(A)^{\frac{1}{n}} + \det(B)^{\frac{1}{n}}$. For a ...
nsoum's user avatar
  • 41