Does $|matrix| _{op} geq |row|_2 +|column|_2$?
$begingroup$
let A be a $m times n$ matrix
$$|A| _2 := sup_{x in S^{n-1}, y in S^{m-1}} <Ax,y>$$
let $r$ denotes first row of $A$ ,and $c$ denotes column of $A$.
then
$$|A| _2 geq |r|_2 +|c|_2$$
where $||_2$ denotes Euclidean norm ,
Is that true?
matrices norm
asked Dec 30 '18 at 16:36
ShaoyuPeiShaoyuPei
1848
$endgroup$
add a comment |
$begingroup$
let A be a $m times n$ matrix
$$|A| _2 := sup_{x in S^{n-1}, y in S^{m-1}} <Ax,y>$$
let $r$ denotes first row of $A$ ,and $c$ denotes column of $A$.
then
$$|A| _2 geq |r|_2 +|c|_2$$
where $||_2$ denotes Euclidean norm ,
Is that true?
matrices norm
asked Dec 30 '18 at 16:36
ShaoyuPeiShaoyuPei
1848
$endgroup$
add a comment |
$begingroup$
let A be a $m times n$ matrix
$$|A| _2 := sup_{x in S^{n-1}, y in S^{m-1}} <Ax,y>$$
let $r$ denotes first row of $A$ ,and $c$ denotes column of $A$.
then
$$|A| _2 geq |r|_2 +|c|_2$$
where $||_2$ denotes Euclidean norm ,
Is that true?
matrices norm
asked Dec 30 '18 at 16:36
ShaoyuPeiShaoyuPei
1848
$endgroup$
let A be a $m times n$ matrix
$$|A| _2 := sup_{x in S^{n-1}, y in S^{m-1}} <Ax,y>$$
let $r$ denotes first row of $A$ ,and $c$ denotes column of $A$.
then
$$|A| _2 geq |r|_2 +|c|_2$$
where $||_2$ denotes Euclidean norm ,
Is that true?
matrices norm
matrices norm
asked Dec 30 '18 at 16:36
ShaoyuPeiShaoyuPei
1848
asked Dec 30 '18 at 16:36
ShaoyuPeiShaoyuPei
1848
edited Dec 30 '18 at 16:44
ShaoyuPei
asked Dec 30 '18 at 16:36
ShaoyuPeiShaoyuPei
1848
asked Dec 30 '18 at 16:36
ShaoyuPeiShaoyuPei
1848
asked Dec 30 '18 at 16:36
ShaoyuPeiShaoyuPei
1848
1848
add a comment |
add a comment |
1 Answer
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$begingroup$
If $A$ is the matrix $pmatrix{0 & 0 \ 0 & 1}$, then the first row and first column have 2-norm $0$, while the operator norm is clearly $1$ (attained by $pmatrix{0 \ 1}$).
answered Dec 30 '18 at 16:52
preferred_anonpreferred_anon
13.1k11843
$endgroup$
add a comment |
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$begingroup$
If $A$ is the matrix $pmatrix{0 & 0 \ 0 & 1}$, then the first row and first column have 2-norm $0$, while the operator norm is clearly $1$ (attained by $pmatrix{0 \ 1}$).
answered Dec 30 '18 at 16:52
preferred_anonpreferred_anon
13.1k11843
$endgroup$
add a comment |
$begingroup$
If $A$ is the matrix $pmatrix{0 & 0 \ 0 & 1}$, then the first row and first column have 2-norm $0$, while the operator norm is clearly $1$ (attained by $pmatrix{0 \ 1}$).
answered Dec 30 '18 at 16:52
preferred_anonpreferred_anon
13.1k11843
$endgroup$
add a comment |
$begingroup$
If $A$ is the matrix $pmatrix{0 & 0 \ 0 & 1}$, then the first row and first column have 2-norm $0$, while the operator norm is clearly $1$ (attained by $pmatrix{0 \ 1}$).
answered Dec 30 '18 at 16:52
preferred_anonpreferred_anon
13.1k11843
$endgroup$
If $A$ is the matrix $pmatrix{0 & 0 \ 0 & 1}$, then the first row and first column have 2-norm $0$, while the operator norm is clearly $1$ (attained by $pmatrix{0 \ 1}$).
answered Dec 30 '18 at 16:52
preferred_anonpreferred_anon
13.1k11843
answered Dec 30 '18 at 16:52
preferred_anonpreferred_anon
13.1k11843
answered Dec 30 '18 at 16:52
preferred_anonpreferred_anon
13.1k11843
answered Dec 30 '18 at 16:52
preferred_anonpreferred_anon
13.1k11843
13.1k11843
add a comment |
add a comment |
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