  We establish sharp well-posedness and approximation estimates for variational
saddle point systems at the continuous level. The main results of this note
have been known to be true only in the finite dimensional case. Known spectral
results from the discrete case are reformulated and proved using a functional
analysis view, making the proofs in both cases, discrete and continuous, less
technical than the known discrete approaches. We focus on analyzing the special
case when the form $a(\cdot, \cdot)$ is bounded, symmetric, and coercive, and
the mixed form $b(\cdot, \cdot)$ is bounded and satisfies a standard
$\inf-\sup$ or LBB condition. We characterize the spectrum of the symmetric
operators that describe the problem at the continuous level. For a particular
choice of the inner product on the product space of $b(\cdot, \cdot)$, we prove
that the spectrum of the operator representing the system at continuous level
is $\left \{\frac{1-\sqrt{5}}{2}, 1, \frac{1+\sqrt{5}}{2} \right \}$. As
consequences of the spectral description, we find the minimal length interval
that contains the ratio between the norm of the data and the norm of the
solution, and prove explicit approximation estimates that depend only on the
continuity constant and the continuous and the discrete $\inf-\sup$ condition
constants.
