# 2014-05 Nonnegative determinant

Let $$n$$, $$k$$ be positive integers and let $$A_1,A_2,\ldots,A_n$$ be $$k\times k$$ real matrices. Prove or disprove that $\det\left(\sum_{i=1}^n A_i^t A_i\right)\ge 0.$  (Here, $$A^t$$ denotes the transpose of the matrix $$A$$.)

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