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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 diagnolized
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 eigenvals  eigenvalues with multiplicities of M
D.3.2.19 minipoly  minimal polynomial of M
D.3.2.20 spnf  normal form of spectrum sp
D.3.2.21 spprint  print spectrum sp
D.3.2.22 jordan  Jordan data of M
D.3.2.23 jordanbasis  Jordan basis and weight filtration of M
D.3.2.24 jordanmatrix  Jordan matrix with Jordan data jd
D.3.2.25 jordannf  Jordan normal form of M