3
$\begingroup$

I'm curious whether anyone knows how $\lambda$ came to be used to represent eigenvalues and or who (if anyone) was responsible for the convention. I've looked through a couple of books on the history of math/notation but haven't found a relevant reference. Did the eigenvalue usage arise from work with wavelengths or quadratic forms?

There is a reference here:

$\lambda_i$ in the normal form of $(Ax,x)$ are the roots of the characteristic polynomial $\det(\lambda I-A)$ [...]

although I'm not sure if that is modern usage put into historical context.

Improve this question
$\endgroup$
3
  • 2
    $\begingroup$ A glance at maths.ed.ac.uk/~v1ranick/sylv/inertia.pdf or archive.org/details/collectedmathem01sylvrich/page/n395/mode/… shows that Sylvester used the $\lambda$ symbol. $\endgroup$
    – kimchi lover
    Commented Feb 12, 2023 at 20:14
  • 1
    $\begingroup$ Check if Lagrange or Cauchy used the notation $\lambda$ or $\lambda_i$ for the coefficients of diagonalized quadratic forms (see the bottom of the 2nd page of Steen's paper in your question). I think if you trace things back in terms of applications, what we speak of today as eigenvalues showed up when diagonalizing quadratic forms, while at the same time some of those coefficients could be described using max/min values via Lagrange multipliers, so I suspect you might find the notation $\lambda$ for eigenvalues comes from the notation $\lambda$ for Lagrange multipliers. $\endgroup$
    – KCd
    Commented Feb 13, 2023 at 5:27
  • $\begingroup$ @KCd I had a peek at both Cauchy (1829, gallica.bnf.fr/ark:/12148/bpt6k90201q/f177 ) and Lagrange Mechanique and it doesn't appear that either used $\lambda$. Found an interesting read here: sciencedirect.com/science/article/pii/… $\endgroup$
    – Scott H.
    Commented Feb 14, 2023 at 16:23

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.