Proof of Cramer's rule with Dirac delta function

June Haak Ee, Jungil Lee, Chaehyun Yu

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We present a new proof of Cramer's rule by interpreting a system of linear equations as a transformation of n-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the original coordinate vector with Dirac delta functions and changing integration variables from the original coordinates to new coordinates. As a byproduct, we derive a generalized version of Cramer's rule that applies to a partial set of variables, which is new to the best of our knowledge. Our formulation of finding a transformation rule for multi-variable functions shall be particularly useful in changing a partial set of generalized coordinates of a mechanical system.

Original languageEnglish
Article number065002
JournalEuropean Journal of Physics
Issue number6
Publication statusPublished - 2020 Nov

Bibliographical note

Publisher Copyright:
© 2020 European Physical Society.


  • Cramer s rule
  • Dirac delta function
  • generalized coordinates

ASJC Scopus subject areas

  • General Physics and Astronomy


Dive into the research topics of 'Proof of Cramer's rule with Dirac delta function'. Together they form a unique fingerprint.

Cite this