norm of difference of two matrices.
$begingroup$
For any two symmetric $ntimes n$ matrices $A$ and $B$, let their eigenvalues be ordered from largest to smallest. How to prove that for eigenvalues
$$|lambda_k^A-lambda_k^B| leq |A-B| text{for} 1leq kleq n$$ where $lambda_k^A, lambda_k^B$ are respective eigen values of $A$ and $B$.
eigenvalues-eigenvectors norm matrix-norms
asked Dec 1 '18 at 8:05
Mittal GMittal G
1,230516
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add a comment |
$begingroup$
For any two symmetric $ntimes n$ matrices $A$ and $B$, let their eigenvalues be ordered from largest to smallest. How to prove that for eigenvalues
$$|lambda_k^A-lambda_k^B| leq |A-B| text{for} 1leq kleq n$$ where $lambda_k^A, lambda_k^B$ are respective eigen values of $A$ and $B$.
eigenvalues-eigenvectors norm matrix-norms
asked Dec 1 '18 at 8:05
Mittal GMittal G
1,230516
$endgroup$
$begingroup$
Which norm are you taking? Is it the operator norm?
$endgroup$
– SinTan1729
Dec 1 '18 at 13:33
$begingroup$
Yes operator norm.
$endgroup$
– Mittal G
Dec 1 '18 at 16:26
add a comment |
$begingroup$
For any two symmetric $ntimes n$ matrices $A$ and $B$, let their eigenvalues be ordered from largest to smallest. How to prove that for eigenvalues
$$|lambda_k^A-lambda_k^B| leq |A-B| text{for} 1leq kleq n$$ where $lambda_k^A, lambda_k^B$ are respective eigen values of $A$ and $B$.
eigenvalues-eigenvectors norm matrix-norms
asked Dec 1 '18 at 8:05
Mittal GMittal G
1,230516
$endgroup$
For any two symmetric $ntimes n$ matrices $A$ and $B$, let their eigenvalues be ordered from largest to smallest. How to prove that for eigenvalues
$$|lambda_k^A-lambda_k^B| leq |A-B| text{for} 1leq kleq n$$ where $lambda_k^A, lambda_k^B$ are respective eigen values of $A$ and $B$.
eigenvalues-eigenvectors norm matrix-norms
eigenvalues-eigenvectors norm matrix-norms
asked Dec 1 '18 at 8:05
Mittal GMittal G
1,230516
asked Dec 1 '18 at 8:05
Mittal GMittal G
1,230516
asked Dec 1 '18 at 8:05
Mittal GMittal G
1,230516
asked Dec 1 '18 at 8:05
Mittal GMittal G
1,230516
asked Dec 1 '18 at 8:05
Mittal GMittal G
1,230516
1,230516
$begingroup$
Which norm are you taking? Is it the operator norm?
$endgroup$
– SinTan1729
Dec 1 '18 at 13:33
$begingroup$
Yes operator norm.
$endgroup$
– Mittal G
Dec 1 '18 at 16:26
add a comment |
$begingroup$
Which norm are you taking? Is it the operator norm?
$endgroup$
– SinTan1729
Dec 1 '18 at 13:33
$begingroup$
Yes operator norm.
$endgroup$
– Mittal G
Dec 1 '18 at 16:26
$begingroup$
Which norm are you taking? Is it the operator norm?
$endgroup$
– SinTan1729
Dec 1 '18 at 13:33
$begingroup$
Which norm are you taking? Is it the operator norm?
$endgroup$
– SinTan1729
Dec 1 '18 at 13:33
$begingroup$
Yes operator norm.
$endgroup$
– Mittal G
Dec 1 '18 at 16:26
$begingroup$
Yes operator norm.
$endgroup$
– Mittal G
Dec 1 '18 at 16:26
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
A proof by Demetres Christofides is given here.
answered Dec 3 '18 at 21:32
Grigorios KostakosGrigorios Kostakos
4617
$endgroup$
add a comment |
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1 Answer
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votes
1 Answer
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active
oldest
votes
active
oldest
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active
oldest
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$begingroup$
A proof by Demetres Christofides is given here.
answered Dec 3 '18 at 21:32
Grigorios KostakosGrigorios Kostakos
4617
$endgroup$
add a comment |
$begingroup$
A proof by Demetres Christofides is given here.
answered Dec 3 '18 at 21:32
Grigorios KostakosGrigorios Kostakos
4617
$endgroup$
add a comment |
$begingroup$
A proof by Demetres Christofides is given here.
answered Dec 3 '18 at 21:32
Grigorios KostakosGrigorios Kostakos
4617
$endgroup$
A proof by Demetres Christofides is given here.
answered Dec 3 '18 at 21:32
Grigorios KostakosGrigorios Kostakos
4617
answered Dec 3 '18 at 21:32
Grigorios KostakosGrigorios Kostakos
4617
answered Dec 3 '18 at 21:32
Grigorios KostakosGrigorios Kostakos
4617
answered Dec 3 '18 at 21:32
Grigorios KostakosGrigorios Kostakos
4617
4617
add a comment |
add a comment |
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$begingroup$
Which norm are you taking? Is it the operator norm?
$endgroup$
– SinTan1729
Dec 1 '18 at 13:33
$begingroup$
Yes operator norm.
$endgroup$
– Mittal G
Dec 1 '18 at 16:26