Minimize a quadratic form over a subspace

Question

I'm learning optimization methods. For the minimization problem:

\begin{align} \min_{x}\,\,x^TAx+b^Tx,&&\mbox{s.t.}\,\,& Cx=d,\\& \end{align}

I was asked to minimize it over some given n-dimensional subspace L subject to the constraint.

I'm not familiar with the subspace concept here. What does it mean to "optimize over the subspace"? Could someone explain it in a more plain language? Thanks.

Updates: If L is a span of vectors $ l_1,l_2,l_3...$, does it mean x must be a linear combination of those vectors?

Answer 1

Presumably they mean that $x$ needs to be in $L,$ that is you need to find $\min_{x|x \in L}$