Is a symmetric matrice allways nonsingular?

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SUMMARY

A symmetric matrix is not always nonsingular, as demonstrated by the zero matrix, which is symmetric but singular. This confirms that the property of being symmetric does not guarantee that a matrix has an inverse. The discussion highlights the need for further exploration of matrix properties to understand singularity and nonsingularity.

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Can someone confirm this? If so, are there any respected websites on the net that can confirm this theorem?
 
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No. Example: The zero matrix is symmetric.
 

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