# On Approximation Problems With Zero-Trace Matrices

@article{Zietak1996OnAP, title={On Approximation Problems With Zero-Trace Matrices}, author={Krystyna Zietak}, journal={Linear Algebra and its Applications}, year={1996}, volume={247}, pages={169-183} }

Abstract We consider some approximation problems in the linear space of complex matrices with respect to unitarily invariant norms. We deal with special cases of approximation of a matrix by zero-trace matrices. Moreover, some characterizations of zero-trace matrices are given by means of matrix approximation problems.

#### 11 Citations

On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm

- Mathematics, Computer Science
- SIAM J. Matrix Anal. Appl.
- 2009

We show that certain matrix approximation problems in the matrix 2-norm have uniquely defined solutions, despite the lack of strict convexity of the matrix 2-norm. The problems we consider are… Expand

Orthogonality to matrix subspaces, and a distance formula

- Mathematics
- 2014

Abstract We obtain a necessary and sufficient condition for a matrix A to be Birkhoff–James orthogonal to any subspace W of M n ( C ) . Using this we obtain an expression for the distance of A from… Expand

A semismooth Newton-CG based dual PPA for matrix spectral norm approximation problems

- Mathematics, Computer Science
- Math. Program.
- 2016

The results show that the proposed semismooth Newton-CG based dual PPA for solving the matrix norm approximation problems substantially outperforms the pure ADMM, especially for the constrained cases and it is able to solve the problems robustly and efficiently to a relatively high accuracy. Expand

A Semismooth Newton-CG Dual Proximal Point Algorithm for Matrix Spectral Norm Approximation Problems

- 2012

We consider a class of matrix spectral norm approximation problems for finding an affine combination of given matrices having the minimal spectral norm subject to some prescribed linear equality and… Expand

From the strict Chebyshev approximant of a vector to the strict spectral approximant of a matrix

- Mathematics
- 2017

The main aim of this review paper is approximation of a complex rectangular matrix, with respect to the unitarily invariant norms, by matrices from a linear subspace or from a convex closed subset of… Expand

On the volume-preserving procrustes problem

- Mathematics
- 2004

This paper is intended to study the volume-preserving procrustes problem arising from practical areas. The corresponding solution should satisfy a matrix equation which is solved by the singular… Expand

Developing the CGLS algorithm for the least squares solutions of the general coupled matrix equations

- Mathematics
- 2014

In the present paper, we consider the minimum norm solutions of the general least squares problem
By developing the conjugate gradient least square (CGLS) method, we construct an… Expand

On the extremal structure of least upper bound norms and their dual

- Mathematics
- 2008

Abstract Given finite dimensional real or complex Banach spaces, E and F, with norms ν : E → R and μ : F → R , we denote by N μ ν the least upper bound norm induced on L ( E , F ) . Some results are… Expand

On Chebyshev Polynomials of Matrices

- Mathematics, Computer Science
- SIAM J. Matrix Anal. Appl.
- 2010

General properties of Chebyshev polynomials of matrices are studied, which in some cases turn out to be generalizations of well-known properties of Chemicals of compact sets in the complex plane. Expand

On the generalized reflexive and anti-reflexive solutions to a system of matrix equations

- Mathematics
- 2012

Let P and Q be two generalized reflection matrices, i.e, P=PH, P2=I and Q=QH, Q2=I. An n×n matrix A is said to be generalized reflexive (generalized anti-reflexive) with respect to the matrix pair… Expand

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