### 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=permutaion,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

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