given four complex matrices a, b, c and d where a 2 cnn and d 2 cmm andlet the matrix(a bc d)be a normal matrix and assume that  is a given complex number that is not eigenvalue of matrix a. we present a method to calculate the distance norm (with respect to 2-norm) from d to the set of matrices x 2 cmm such that,  be a multiple eigenvalue of matrix(a bc x). we also nd the nearest matrix ...

Let G be a linear algebraic group acting linearly on vector space (or more generally, an affine variety) V, and let k[V]G the corresponding algebra of invariant polynomial functions. A separating set S⊆k[V]G is polynomials with property that for all v,w∈V, if there exists f∈k[V]G $v$ $w$, then f∈S $w$. In this article, we consider action G=GL2⁡(C) C-vector M2n n-tuples 2×2 matrices by simultane...