ThmDex – An index of mathematical definitions, results, and conjectures.
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Deduction system
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Zermelo-Fraenkel set theory
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Square matrix
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Complex matrix square root
Definition D5192
Real matrix square root
Formulation 0
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix.
A D6160: Real square matrix $B \in \mathbb{R}^{N \times N}$ is a square root for $A$ if and only if \begin{equation} A = B^2 \end{equation}
Formulation 1
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix.
A D6160: Real square matrix $B \in \mathbb{R}^{N \times N}$ is a square root for $A$ if and only if \begin{equation} A = B B \end{equation}