Linear algebra via complex analysis

Alexander P. Campbell, Daniel Daners

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The resolvent (λIA)−1 of a matrix A is naturally an analytic function of λ ∈ ℂ, and the eigenvalues are isolated singularities. We compute the Laurent expansion of the resolvent about the eigenvalues of A. Using the Laurent expansion, we prove the Jordan decomposition theorem, prove the Cayley–Hamilton theorem, and determine the minimal polynomial of A. The proofs do not make use of determinants, and many results naturally generalize to operators on Banach spaces.
Original languageEnglish
Pages (from-to)877-892
Number of pages16
JournalAmerican Mathematical Monthly
Issue number10
Publication statusPublished - Dec 2013
Externally publishedYes


Dive into the research topics of 'Linear algebra via complex analysis'. Together they form a unique fingerprint.

Cite this