What is the sign of Ax where A is negative definite matrix and x > 0?

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Tomoki Matsumoto

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Tomoki Matsumoto Asks: What is the sign of Ax where A is negative definite matrix and x > 0?
Let A be a negative definite matrix and x is a vector whose elements are positive all, that is x > 0. Then, is the sign of all elements of the vector Ax negative?

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