Project ForgeEngineering Mathematics
Linear Algebra
GATE 2020
Easy
Let I be a 100-dimensional identity matrix and E be the set of its distinct (no value appears more than once in E) real eigenvalues. The number of elements in E is __________.
1(± 0.1 accepted)
Explanation
Every eigenvalue of an identity matrix (of any dimension) equals 1, with algebraic multiplicity equal to the matrix's dimension. Since only distinct values are counted, the set E contains exactly one element: {1}.
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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