We know that
$(AB)^T=B^TA^T$.
Thus:
$(A^TA)^T=(A)^T(A^T)^T=A^TA$.
Is this correct? I never realize this could be true. Is there a name to this property?
2026-03-28 00:06:20.1774656380
Transpose of the product of a transpose matrix and itself
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Yes, it is true. Any matrix $B$ that satisfies $B^T=B$, is called a symmetric matrix. In fact, given a matrix $A$, the matrix $B=A^TA$ is always symmetric, as you have shown. That is a standard procedure to obtain symmetric matrices.