Infrastructure for Manipulation Polynomial Matrices
Adjungate or classical adjoint of a square matrix
Combine polynomial matrices by rows or columns
Characteristic polynomial of a matrix
Cofactor of a matrix
Gets the maximum degree of polynomial objects
Polynomial matrix Diagonals Extract or construct a diagonal polynomial...
GCD for polynomial matrices
Inverse polynomial matrix
Check if object is polyMatrix
Proper polynomial matrices
Tests if something is zero or not
LCM for polynomial matrices
Degree of each item of the matrix
Minor of matrix item
Build matrix of polynimal decomposition using Newton interpolation in ...
Parse polynomial matrix from strings
Parse polynomial from string
Arithmetic Operators
A class to represent a matrix of polynomials
Matrix multiplication
Implementation of matrices of polynomials
Extract or Replace Parts of a polynomial matrix
Apply for polynomial matrix
Create polyMatrix object
A class to repesent characteristic polynomial of a polynomial matrix
Polynomial matrix transpose
Trace of a 'matrix' or 'polyMatrix' class matrix
Triangularization of a polynomial matrix by interpolation method
Triangularization of a polynomial matrix by Sylvester method
Rounds objects to zero if there is too small
Get zero lead hyper rows of size sub_nrow of matrix M
Get zero lead rows of matrix M
Implementation of class "polyMatrix" for storing a matrix of polynomials and implements basic matrix operations; including a determinant and characteristic polynomial. It is based on the package 'polynom' and uses a lot of its methods to implement matrix operations. This package includes 3 methods of triangularization of polynomial matrices: Extended Euclidean algorithm which is most classical but numerically unstable; Sylvester algorithm based on LQ decomposition; Interpolation algorithm is based on LQ decomposition and Newton interpolation. Both methods are described in D. Henrion & M. Sebek, Reliable numerical methods for polynomial matrix triangularization, IEEE Transactions on Automatic Control (Volume 44, Issue 3, Mar 1999, Pages 497-508) <doi:10.1109/9.751344> and in Salah Labhalla, Henri Lombardi & Roger Marlin, Algorithmes de calcule de la reduction de Hermite d'une matrice a coefficients polynomeaux, Theoretical Computer Science (Volume 161, Issue 1-2, July 1996, Pages 69-92) <doi:10.1016/0304-3975(95)00090-9>.