Katkat
Back

Derive eigenvalues and sum for inverse matrix

DRWData Scientist · Onsite
EasyData ScientistOnsiteStatistics & Math

Last updated

Derive eigenvalues and sum for inverse matrix evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Let A be an invertible n×n matrix with eigenvalues {λ1, …, λn} (all nonzero). Prove that the eigenvalues of A^{-1} are {1/λ1, …, 1/λn}. Then compute the sum of the eigenvalues of A^{-1} and express it in terms of A (e.g., as tr(A^{-1})); discuss any assumptions needed for these equalities to hold.