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Easy · Data Science · Quant Trader interview question · linear-algebra, determinant, inverse, matrix
You are building a statistical arbitrage model that relies on inverting covariance matrices. Your model throws an error because the determinant of a covariance matrix, $A$, is close to zero. You decide to regularize the matrix, but before doing so, you want to understand the effect of the determinant of the inverse matrix, $A^{-1}$. Given a matrix $A$ with a non-zero determinant, what is $\det(A^{-1})$ expressed in terms of $\det(A)$?