Notation for eigenvalues












0












$begingroup$


Is there a specific notation for eigenvalues? specifically, I'd like to write:
$$mequiv text{smallest eigenvaue of }H$$
I've seen some sources write this as: $Hsucceq mI$, where "$succeq0$" means the matrix is semi positive definite, but it seems a bit convoluted.



Is there a simpler, more accepted way to write this?






notation eigenvalues-eigenvectors







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  • 1




    $begingroup$
    I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
    $endgroup$
    – Gregory Grant
    Dec 26 '15 at 15:03








  • 1




    $begingroup$
    What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
    $endgroup$
    – A.P.
    Dec 26 '15 at 15:07


















0












$begingroup$


Is there a specific notation for eigenvalues? specifically, I'd like to write:
$$mequiv text{smallest eigenvaue of }H$$
I've seen some sources write this as: $Hsucceq mI$, where "$succeq0$" means the matrix is semi positive definite, but it seems a bit convoluted.



Is there a simpler, more accepted way to write this?






notation eigenvalues-eigenvectors







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
    $endgroup$
    – Gregory Grant
    Dec 26 '15 at 15:03








  • 1




    $begingroup$
    What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
    $endgroup$
    – A.P.
    Dec 26 '15 at 15:07
















0












0








0





$begingroup$


Is there a specific notation for eigenvalues? specifically, I'd like to write:
$$mequiv text{smallest eigenvaue of }H$$
I've seen some sources write this as: $Hsucceq mI$, where "$succeq0$" means the matrix is semi positive definite, but it seems a bit convoluted.



Is there a simpler, more accepted way to write this?






notation eigenvalues-eigenvectors







share|cite|improve this question









$endgroup$




Is there a specific notation for eigenvalues? specifically, I'd like to write:
$$mequiv text{smallest eigenvaue of }H$$
I've seen some sources write this as: $Hsucceq mI$, where "$succeq0$" means the matrix is semi positive definite, but it seems a bit convoluted.



Is there a simpler, more accepted way to write this?






notation eigenvalues-eigenvectors




notation eigenvalues-eigenvectors






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 26 '15 at 15:01









nbubisnbubis

27.3k552110




27.3k552110








  • 1




    $begingroup$
    I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
    $endgroup$
    – Gregory Grant
    Dec 26 '15 at 15:03








  • 1




    $begingroup$
    What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
    $endgroup$
    – A.P.
    Dec 26 '15 at 15:07
















  • 1




    $begingroup$
    I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
    $endgroup$
    – Gregory Grant
    Dec 26 '15 at 15:03








  • 1




    $begingroup$
    What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
    $endgroup$
    – A.P.
    Dec 26 '15 at 15:07










1




1




$begingroup$
I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
$endgroup$
– Gregory Grant
Dec 26 '15 at 15:03






$begingroup$
I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
$endgroup$
– Gregory Grant
Dec 26 '15 at 15:03






1




1




$begingroup$
What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
$endgroup$
– A.P.
Dec 26 '15 at 15:07






$begingroup$
What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
$endgroup$
– A.P.
Dec 26 '15 at 15:07












1 Answer
1






active

oldest

votes


















1












$begingroup$

Normally one says something like "Let $lambda_1, ldots, lambda_n$ be the eigenvalues of $H$ in non-decreasing order." or "Let $lambda_1 leq ldotsleq lambda_n$ be the eigenvalues of $H$."



Then, you just say $lambda_1$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    I take this as "no".
    $endgroup$
    – nbubis
    Dec 29 '15 at 10:08










  • $begingroup$
    Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
    $endgroup$
    – Batman
    Dec 29 '15 at 15:46













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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









1












$begingroup$

Normally one says something like "Let $lambda_1, ldots, lambda_n$ be the eigenvalues of $H$ in non-decreasing order." or "Let $lambda_1 leq ldotsleq lambda_n$ be the eigenvalues of $H$."



Then, you just say $lambda_1$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    I take this as "no".
    $endgroup$
    – nbubis
    Dec 29 '15 at 10:08










  • $begingroup$
    Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
    $endgroup$
    – Batman
    Dec 29 '15 at 15:46


















1












$begingroup$

Normally one says something like "Let $lambda_1, ldots, lambda_n$ be the eigenvalues of $H$ in non-decreasing order." or "Let $lambda_1 leq ldotsleq lambda_n$ be the eigenvalues of $H$."



Then, you just say $lambda_1$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    I take this as "no".
    $endgroup$
    – nbubis
    Dec 29 '15 at 10:08










  • $begingroup$
    Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
    $endgroup$
    – Batman
    Dec 29 '15 at 15:46
















1












1








1





$begingroup$

Normally one says something like "Let $lambda_1, ldots, lambda_n$ be the eigenvalues of $H$ in non-decreasing order." or "Let $lambda_1 leq ldotsleq lambda_n$ be the eigenvalues of $H$."



Then, you just say $lambda_1$.






share|cite|improve this answer









$endgroup$



Normally one says something like "Let $lambda_1, ldots, lambda_n$ be the eigenvalues of $H$ in non-decreasing order." or "Let $lambda_1 leq ldotsleq lambda_n$ be the eigenvalues of $H$."



Then, you just say $lambda_1$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 26 '15 at 15:04









BatmanBatman

16.5k11735




16.5k11735












  • $begingroup$
    I take this as "no".
    $endgroup$
    – nbubis
    Dec 29 '15 at 10:08










  • $begingroup$
    Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
    $endgroup$
    – Batman
    Dec 29 '15 at 15:46




















  • $begingroup$
    I take this as "no".
    $endgroup$
    – nbubis
    Dec 29 '15 at 10:08










  • $begingroup$
    Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
    $endgroup$
    – Batman
    Dec 29 '15 at 15:46


















$begingroup$
I take this as "no".
$endgroup$
– nbubis
Dec 29 '15 at 10:08




$begingroup$
I take this as "no".
$endgroup$
– nbubis
Dec 29 '15 at 10:08












$begingroup$
Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
$endgroup$
– Batman
Dec 29 '15 at 15:46






$begingroup$
Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
$endgroup$
– Batman
Dec 29 '15 at 15:46




















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