16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 3.7.5

Linear Transformations

Mathematics — Linear Algebra · matrix-zero-trace-criterion

Problem

Let AA be an m×nm \times n matrix with real entries. Prove that A=0A = 0 if and only if trace⁡(AtA)=0\operatorname{trace}(A^t A) = 0.

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