Would really appreciate if someone can explain:
$$ (\|Mx\|_2)^2 = (M^Tx)^T(M^Tx) $$
can't get my head round with this.
2026-04-01 23:55:41.1775087741
Explain $(\|Mx\|_2)^2 = (M^Tx)^T(M^Tx) $ (positive definite, positive semi definite)
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Note that if $u,v$ are column vectors of the same size, $$ \langle u,v \rangle = u_1v_1 + \cdots + u_n v_n = v^Tu = u^Tv $$ Note, then, that $$ \|u\|^2 = \langle u,u \rangle = u^Tu $$ now, set $u = Mx$.