## 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