LinBox
Summary
LinBox is a C++ template library for exact, high-performance linear algebra computation with dense, sparse, and structured matrices over the integers and over finite fields. LinBox has the following top-level functions: solve linear system, matrix rank, determinant, minimal polynomial, characteristic polynomial, Smith normal form and trace. A good collection of finite field and ring implementations is provided, for use with numerous black box matrix storage schemes.
Authors
The LinBox team
Status
officially approved by the authors
Aims and scope
Mathematical Classification
Keywords
- blackbox matrices
- Blackbox matrix algorithms
- canonical forms
- characteristic polynomial
- characteristic polynomials
- computational linear algebra
- computer algebra
- dense matrices
- dense systems
- determinants
- Diophantine systems
- eigenvalues
- eigenvectors
- exact arithmetic
- exact computational results
- exact linear algebra
- factorizations
- finite fields
- finite rings
- Frobenius form
- gaussian algorithm
- generic library
- integer arithmetics
- integers
- least-norm solutions
- least-squares solutions
- linear algebra
- linear equation system solver
- matrices
- matrix
- matrix factorization
- matrix rank
- minimal polynomials
- nonsingular system
- normal forms
- p-adic lifting
- positive definiteness determination
- quotient fields
- Smith form
- Smith normal forms
- sparse matrices
- sparse systems
- structured matrices
- symbolic linear algebra
- symbolic-numerical solving