Minimizing the error cost is done by taking the derivative wrt c so y=c.

I understand in the matrix case E(c) = T(e)e where T( ) is the transpose . where y=Hc+e

= T(y-Hc) (y-Hc) = T(y)y -T( x)Hy -T(y)Hx +T(x)T(H)Hx .

The derivative wrt x is -2T(y)H+2T(x)T(H)H= 0 => x=inverse(T(H)H)*T(H)y

I guess I am just confused on the scalar case on what to do.