D.3.2 linalg_lib

Library:

linalg.lib

Purpose:

Algorithmic Linear Algebra

Authors:

Ivor Saynisch (ivs@math.tu-cottbus.de)
Mathias Schulze (mschulze@mathematik.uni-kl.de)

Procedures:

D.3.2.1 inverse		matrix, the inverse of A
D.3.2.2 inverse_B		list(matrix Inv,poly p),Inv*A=p*En ( using busadj(A) )
D.3.2.3 inverse_L		list(matrix Inv,poly p),Inv*A=p*En ( using lift )
D.3.2.4 sym_gauss		symmetric gaussian algorithm
D.3.2.5 orthogonalize		Gram-Schmidt orthogonalization
D.3.2.6 diag_test		test whether A can be diagonalized
D.3.2.7 busadj		coefficients of Adj(E*t-A) and coefficients of det(E*t-A)
D.3.2.8 charpoly		characteristic polynomial of A ( using busadj(A) )
D.3.2.9 adjoint		adjoint of A ( using busadj(A) )
D.3.2.10 det_B		determinant of A ( using busadj(A) )
D.3.2.11 gaussred		gaussian reduction: P*A=U*S, S a row reduced form of A
D.3.2.12 gaussred_pivot		gaussian reduction: P*A=U*S, uses row pivoting
D.3.2.13 gauss_nf		gaussian normal form of A
D.3.2.14 mat_rk		rank of constant matrix A
D.3.2.15 U_D_O		P*A=U*D*O, P,D,U,O=permutation,diag,lower-,upper-triang
D.3.2.16 pos_def		test symmetric matrix for positive definiteness
D.3.2.17 hessenberg		Hessenberg form of M
D.3.2.18 evnf		eigenvalues normal form of (e[,m])
D.3.2.19 eigenvals		eigenvalues with multiplicities of M
D.3.2.20 minipoly		minimal polynomial of M
D.3.2.21 jordan		Jordan data of M
D.3.2.22 jordanbasis		Jordan basis and weight filtration of M
D.3.2.23 jordanmatrix		Jordan matrix with Jordan data (e,s,m)
D.3.2.24 jordannf		Jordan normal form of M