A new tag: singularvalues. The name of the tags seems a bit different than usual - I would expect it to be singular-values, which would reflect other tags consisting from two words. The tag-info is currently empty. Is it worth keeping? Will it be useful?
I am wondering whether there is a meaningful upper bound on the condition number when we restrict ourselves to the following type of matrix:
$\textbf M \in \mathbb Z^{m \times n}$ is a column full rank matrix.
All the entries in $\textbf M$ are in the interval $[0, a]$ for some $a\in \mathbb N$...
Theorem: Suppose $U,V$ are orthogonal subspaces spans $X$, let $A:U\to U,B:V\to V$. then the operator $C=\begin{pmatrix}A&0\\0&B\end{pmatrix}:X\to X$
and $\|C\|=\max\{\|A\|,\|B\|\}$
using above theorem I am told to show the following
$A$ be any linear operator on finite dimensional vector spac...
Theorem: Suppose $U,V$ are orthogonal subspaces spans $X$, let $A:U\to U,B:V\to V$. then the operator $C=\begin{pmatrix}A&0\\0&B\end{pmatrix}:X\to X$
and $\|C\|=\max\{\|A\|,\|B\|\}$
using above theorem I am told to show the following
$A$ be any linear operator on finite dimensional vector spac...
