In this context, a regulator is a map from the algebraic K-theory of an

algebraic variety to a suitable cohomology theory such as etale cohomology or Deligne cohomology.

Put differently: The underlying manifold of an

algebraic variety does not determine these invariants," he added.

It is the purpose of the present paper to investigate the structured distance of a real irreducible tridiagonal matrix to the algebraic variety of real normal irreducible tridiagonal matrices, which we denote by I.

Section 2 introduces notation used throughout the paper, section 3 presents an upper bound for the distance in the Frobenius norm of a real tridiagonal matrix to the algebraic variety of real normal tridiagonal matrices.

N the algebraic variety of the normal real matrices in [R.

We start in Section 2 with the definition of the arc space of an algebraic variety as the set of formal power series solutions (in one variable) to the defining equations of the variety.

The arc space of the algebraic variety X defined by f is the set of power series solutions x(t) = ([x.

which describes a point on our algebraic variety X.

Finally, we outline (Section 6) an alternative interpretation of the higher critical groups as discrete analogues of the Chow groups of an algebraic variety.

An area for further research is to interpret the higher-dimensional critical groups of a simplicial complex [DELTA] as simplicial analogues of the Chow groups of an algebraic variety.