Can we find a natural norm smaller than the infinite norm for this special matrix?
$begingroup$
Let $hat{bf H}$ be a $phat{N}times p hat{N}$ sparse matrix consisting of $ptimes p$ blocks, where each block is of size $hat{N}timeshat{N}$. The values in $hat{bf H}$ is illustrated below (empty places are zero):
The infinite norm of $hat{bf H}$ is obviously 1, and I know infinite norm is no larger than any $p$-norm. My question is, is there an even smaller natural norm for this $hat{bf H}$?
The proof that infinite norm is no larger than any $p$-norm.
linear-algebra norm
asked Dec 8 '18 at 5:50
TonyTony
1,7741828
$endgroup$
add a comment |
$begingroup$
Let $hat{bf H}$ be a $phat{N}times p hat{N}$ sparse matrix consisting of $ptimes p$ blocks, where each block is of size $hat{N}timeshat{N}$. The values in $hat{bf H}$ is illustrated below (empty places are zero):
The infinite norm of $hat{bf H}$ is obviously 1, and I know infinite norm is no larger than any $p$-norm. My question is, is there an even smaller natural norm for this $hat{bf H}$?
The proof that infinite norm is no larger than any $p$-norm.
linear-algebra norm
asked Dec 8 '18 at 5:50
TonyTony
1,7741828
$endgroup$
add a comment |
$begingroup$
Let $hat{bf H}$ be a $phat{N}times p hat{N}$ sparse matrix consisting of $ptimes p$ blocks, where each block is of size $hat{N}timeshat{N}$. The values in $hat{bf H}$ is illustrated below (empty places are zero):
The infinite norm of $hat{bf H}$ is obviously 1, and I know infinite norm is no larger than any $p$-norm. My question is, is there an even smaller natural norm for this $hat{bf H}$?
The proof that infinite norm is no larger than any $p$-norm.
linear-algebra norm
asked Dec 8 '18 at 5:50
TonyTony
1,7741828
$endgroup$
Let $hat{bf H}$ be a $phat{N}times p hat{N}$ sparse matrix consisting of $ptimes p$ blocks, where each block is of size $hat{N}timeshat{N}$. The values in $hat{bf H}$ is illustrated below (empty places are zero):
The infinite norm of $hat{bf H}$ is obviously 1, and I know infinite norm is no larger than any $p$-norm. My question is, is there an even smaller natural norm for this $hat{bf H}$?
The proof that infinite norm is no larger than any $p$-norm.
linear-algebra norm
linear-algebra norm
asked Dec 8 '18 at 5:50
TonyTony
1,7741828
asked Dec 8 '18 at 5:50
TonyTony
1,7741828
edited Dec 8 '18 at 16:02
Tony
asked Dec 8 '18 at 5:50
TonyTony
1,7741828
asked Dec 8 '18 at 5:50
TonyTony
1,7741828
asked Dec 8 '18 at 5:50
TonyTony
1,7741828
1,7741828
add a comment |
add a comment |
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