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linear algebra - Under what conditions does a matrix $A$ have a square root? - Mathematics Stack Exchange

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Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Under what conditions does a matrix 𝐴 𝐴 have a square root? I saw somewhere that this is true for Hermitian positive definite matrices(whose definition I just looked up). Moreover, is it possible that for some subspace 𝑋⊂ 𝑀 𝑛 (ℝ) 𝑋 ⊂ 𝑀 𝑛 ( 𝑅 ) of 𝑛×𝑛 𝑛 × 𝑛 matrices over ℝ 𝑅 , the map 𝐴↦ 𝐴 ‾ ‾ √ 𝐴 ↦ 𝐴 is continuous? People who want to consider more generality can also look at matrices over ℂ 𝐶 . Thank you. Over the complex numbers (or any other algebraica

linear algebra - Under what conditions does a matrix $A$ have a square root? - Mathematics Stack Exchange Stack Internal Knowledge at work Bring the best of human thought and AI automation together at your work. Explore Stack Internal Under what conditions does a matrix $A$ have a square root? Ask Question Asked 14 years, 10 months ago Modified 6 years, 9 months ago Viewed 18k times 33 $\begingroup$ Under what conditions does a matrix $A$ have a square root? I saw somewhere that this is true for Hermitian positive definite matrices(whose definition I just looked up). Moreover, is it possible t

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