a generalized eigenvalue related inequality $frac{{{x^T}{A^{ - T}}PAx}}{{{x^T}Px}} le frac{1}{{{{left| A...
$begingroup$
Does the following inequality always hold? $frac{{{x^T}{A^{ - T}}PAx}}{{{x^T}Px}} le frac{1}{{{{left| A right|}^2}}}$, where A is a invertible matrix and P is a positive-definite matrix, x is a column vertor.
matrices
asked Dec 4 '18 at 7:55
wenbowenbo
293
$endgroup$
add a comment |
$begingroup$
Does the following inequality always hold? $frac{{{x^T}{A^{ - T}}PAx}}{{{x^T}Px}} le frac{1}{{{{left| A right|}^2}}}$, where A is a invertible matrix and P is a positive-definite matrix, x is a column vertor.
matrices
asked Dec 4 '18 at 7:55
wenbowenbo
293
$endgroup$
$begingroup$
When writing |A| do you mean the determinant of $A$ or the norm of $A$, and in this case which norm ?
$endgroup$
– Jean Marie
Dec 4 '18 at 23:57
$begingroup$
It means the determinant of A
$endgroup$
– wenbo
Dec 5 '18 at 1:19
add a comment |
$begingroup$
Does the following inequality always hold? $frac{{{x^T}{A^{ - T}}PAx}}{{{x^T}Px}} le frac{1}{{{{left| A right|}^2}}}$, where A is a invertible matrix and P is a positive-definite matrix, x is a column vertor.
matrices
asked Dec 4 '18 at 7:55
wenbowenbo
293
$endgroup$
Does the following inequality always hold? $frac{{{x^T}{A^{ - T}}PAx}}{{{x^T}Px}} le frac{1}{{{{left| A right|}^2}}}$, where A is a invertible matrix and P is a positive-definite matrix, x is a column vertor.
matrices
matrices
asked Dec 4 '18 at 7:55
wenbowenbo
293
asked Dec 4 '18 at 7:55
wenbowenbo
293
asked Dec 4 '18 at 7:55
wenbowenbo
293
asked Dec 4 '18 at 7:55
wenbowenbo
293
asked Dec 4 '18 at 7:55
wenbowenbo
293
293
$begingroup$
When writing |A| do you mean the determinant of $A$ or the norm of $A$, and in this case which norm ?
$endgroup$
– Jean Marie
Dec 4 '18 at 23:57
$begingroup$
It means the determinant of A
$endgroup$
– wenbo
Dec 5 '18 at 1:19
add a comment |
$begingroup$
When writing |A| do you mean the determinant of $A$ or the norm of $A$, and in this case which norm ?
$endgroup$
– Jean Marie
Dec 4 '18 at 23:57
$begingroup$
It means the determinant of A
$endgroup$
– wenbo
Dec 5 '18 at 1:19
$begingroup$
When writing |A| do you mean the determinant of $A$ or the norm of $A$, and in this case which norm ?
$endgroup$
– Jean Marie
Dec 4 '18 at 23:57
$begingroup$
When writing |A| do you mean the determinant of $A$ or the norm of $A$, and in this case which norm ?
$endgroup$
– Jean Marie
Dec 4 '18 at 23:57
$begingroup$
It means the determinant of A
$endgroup$
– wenbo
Dec 5 '18 at 1:19
$begingroup$
It means the determinant of A
$endgroup$
– wenbo
Dec 5 '18 at 1:19
add a comment |
0
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$begingroup$
When writing |A| do you mean the determinant of $A$ or the norm of $A$, and in this case which norm ?
$endgroup$
– Jean Marie
Dec 4 '18 at 23:57
$begingroup$
It means the determinant of A
$endgroup$
– wenbo
Dec 5 '18 at 1:19