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Fixed a mathematical typo in the third bullet point in the section on Takagi's factorization |
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*Applicable to: square, complex, symmetric matrix ''A''.
*Decomposition: <math>A=VDV^\mathsf{T}</math>, where ''D'' is a real nonnegative [[diagonal matrix]], and ''V'' is [[unitary matrix|unitary]]. <math>V^\mathsf{T}</math> denotes the [[matrix transpose]] of ''V''.
*Comment: The diagonal elements of ''D'' are the nonnegative square roots of the eigenvalues of <math>AA^*=VD^2V^
*Comment: ''V'' may be complex even if ''A'' is real.
*Comment: This is not a special case of the eigendecomposition (see above), which uses <math>V^{-1}</math> instead of <math>V^\mathsf{T}</math>. Moreover, if ''A'' is not real, it is not Hermitian and the form using <math>V^*</math> also does not apply.
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